Selected Title s i n Thi s Subserie s

37 Pete r Kuchmen t an d Vladimi r Lin , Editors , Voronez h Winte r Mathematica l School s

(Dedicated t o Seli m Krein ) (TRANS2/184 )

36 V . E . Zakharov , Editor , Nonlinea r Wave s an d Wea k Turbulenc e (TRANS2/182 )

35 G . I . Olshanski , Editor , Kirillov' s Semina r o n Representatio n Theor y (TRANS2/181 )

34 A . Khovanskii , A . Varchenko , an d V . Vassil iev , Editors , Topic s i n Singularit y

Theory (TRANS2/180 )

33 V . M . Buchstabe r an d S . P . Novikov , Editors , Solitons , Geometry , an d Topology : O n

the Crossroa d (TRANS2/179 )

32 R . L . Dobrushin , R . A . Minlos , M . A . Shubin , an d A . M . Vershik , Editors , Topics i n Statistica l an d Theoretica l Physic s (F . A . Berezi n Memoria l Volume )

(TRANS2/177)

31 R . L . Dobrushin , R . A . Minlos , M . A . Shubin , an d A . M . Vershik , Editors ,

Contemporary Mathematica l Physic s (F . A . Berezi n Memoria l Volume ) (TRANS2/175 )

30 A . A . Bolibruch , A . S . Merkur'ev , an d N . Yu . Ne t sve taev , Editors , Mathematic s

in St . Petersbur g (TRANS2/174 )

29 V . Kharlamov , A . Korchagin , G . PolotovskiT , an d O . Viro , Editors , Topolog y o f

Real Algebrai c Varietie s an d Relate d Topic s (TRANS2/173 )

28 L . A . Bunimovich , B . M . Gurevich , an d Ya . B . Pes in , Editors , Sinai' s Mosco w

Seminar o n Dynamica l System s (TRANS2/171 )

27 S . P . Novikov , Editor , Topic s i n Topolog y an d Mathematica l Physic s (TRANS2/170 )

26 S . G . Gindiki n an d E . B . Vinberg , Editors , Li e Group s an d Li e Algebras : E . B .

Dynkin's Semina r (TRANS2/169 )

25 V . V . Kozlov , Editor , Dynamica l System s i n Classica l Mechanic s (TRANS2/168 )

24 V . V . Lychagin , Editor , Th e Interpla y betwee n Differentia l Geometr y an d Differentia l

Equations (TRANS2/167 )

23 Yu . I lyashenk o an d S . Yakovenko , Editors , Concernin g th e Hilber t 16t h Proble m

(TRANS2/165)

22 N . N . Uraltseva , Editor , Nonlinea r Evolutio n Equation s (TRANS2/164 )

Published Earlie r a s Advance s i n Sovie t Mathematic s 21 V . I . Arnold , Editor , Singularitie s an d bifurcations , 199 4

20 R . L . Dobrushin , Editor , Probabilit y contribution s t o statistica l mechanics , 199 4

19 V . A . Marchenko , Editor , Spectra l operato r theor y an d relate d topics , 199 4

18 Ole g Viro , Editor , Topolog y o f manifold s an d varieties , 199 4

17 D m i t r y Fuchs , Editor , Unconventiona l Li e algebras , 199 3

16 Serge i Gelfan d an d Simo n Gindikin , Editors , I . M . Gelfan d seminar , Part s 1 and 2 ,

1993

15 A . T . Fomenko , Editor , Minima l surfaces , 199 3

14 Yu . S . Il'yashenko , Editor , Nonlinea r Stoke s phenomena , 199 2

13 V . P . Maslo v an d S . N . Samborskit , Editors , Idempoten t analysis , 199 2

12 Ft . Z . Khasminskii , Editor , Topic s i n nonparametri c estimation , 199 2

11 B . Ya . Levin , Editor , Entir e an d subharmoni c functions , 199 2

10 A . V . Babi n an d M . I . Vishik , Editors , Propertie s o f globa l attractor s o f partia l

differential equations , 199 2

9 A . M . Vershik , Editor , Representatio n theor y an d dynamica l systems , 199 2

8 E . B . Vinberg , Editor , Li e groups , thei r discret e subgroups , an d invarian t theory , 199 2

7 M . Sh . Birman , Editor , Estimate s an d asymptotic s fo r discret e spectr a o f integra l an d

differential equations , 199 1

(Continued in the back of this publication)

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Voronezh Winte r Mathematical School s Dedicated t o Selim Krei n

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American Mathematica l Societ y

TRANSLATIONS Series 2 • Volum e 18 4

Advances in the Mathematical Sciences—37

(Formerly Advances in Soviet Mathematics)

Voronezh Winte r Mathematical School s Dedicated t o Seli m Krei n

Peter Kuchmen t Vladimir Li n Editors

American Mathematica l Societ y Providence, Rhod e Islan d

http://dx.doi.org/10.1090/trans2/184

ADVANCES I N TH E MATHEMATICA L SCIENCE S EDITORIAL COMMITTE E

V. I . ARNOL D S. G . GINDIKI N V. P . MASLO V

Translation edite d by Tanya Khovanova

1991 Mathematics Subject Classification. Primar y 35-06 , 47-06, 58-06.

ABSTRACT. Thi s volume , dedicate d t o Professo r Seli m Krei n o n hi s 80t h birthday , contain s pa -pers o n variou s topic s i n mathematics , includin g partia l differentia l equations , operato r theory , function theory , globa l analysis , an d geometr y o f th e Mandelbro t set . I t ca n b e use d b y researc h mathematicians workin g i n thes e area s o f mathematics .

Library o f Congres s Car d Numbe r 91-64074 1 ISBN 0-8218-0976- 8

ISSN 0065-929 0

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Contents

Introduction P E T E R KUCHMEN T AN D VLADIMI R LI N i x

Selim Grigorievic h Krei n P E T E R KUCHMEN T xii i

List o f Publications b y Seli m Krei n xvi i

Fredholm Propert y o f Functiona l Equation s wit h Affin e Transformation s o f Argument GENRICH BELITSKI I AN D VADI M TKACHENK O 1

Construction o f Generalize d Translatio n Operator s fro m th e Syste m o f Appell Character s YURI J M . BEREZANSK Y 7

Witten Deformatio n o f the Analyti c Torsio n an d th e Reidemeiste r Torsio n DAN BURGHELEA , LEONI D FRIEDLANDER , AN D THOMA S KAPPELE R 2 3

Formal Operato r Powe r Serie s an d th e Noncommutativ e Taylo r Formul a YURI L . DALETSKI I 4 1

Plane Curve s wit h a Bi g Fundamenta l Grou p o f the Complemen t GERD DETHLOFF , STEPA N OREVKOV , AN D MIKHAI L ZAIDENBER G 6 3

Solution o f the Linearize d Invers e Conductivit y Proble m i n a Hal f Spac e vi a Integral Geometr y BUMA FRIDMAN , P E T E R KUCHMENT , DAOWE I M A , AN D VASSILI S G .

PAPANICOLAOU 8 5

Almost Periodi c Factorization : Applicabilit y o f the Divisio n Algorith m MARK GELFAN D AN D ILY A M . SPITKOVSK Y 9 7

Liouville an d Caratheodor y Covering s i n Riemannia n an d Comple x Geometry VLADIMIR YA . LI N AN D MIKHAI L ZAIDENBER G 11 1

How Big I s the Se t o f Infinitely Renormalizabl e Quadratics ? MIKHAIL LYUBIC H 13 1

Linear Operator s i n One-dimensiona l Extension s o f Banach Space s YURI LYUBIC H 14 5

viii C O N T E N T S

Random Rearrangement s an d Operator s STEPHEN MONTGOMERY-SMIT H AN D EVGUEN I SEMENO V 15 7

On Reiteratio n Theorem s VLADIMIR I . OVCHINNIKO V 18 5

Statistical Homogenizatio n Theore m fo r Multivalue d Monoton e Ellipti c Operators ALEXANDER PANKO V 19 9

Reconstruction o f Paley-Wiener Function s o n th e Heisenber g Grou p ISSAC PESENSO N 20 7

De Rham Theore m fo r Extende d L 2-Cohomology MIKHAIL SHUBI N 21 7

On th e Discret e Spectru m o f a Clas s o f Problem s Involvin g th e Neuman n Laplacian i n Unbounde d Domain s MICHAEL SOLOMYA K 23 3

Szego-type Extrema l Problem s NAHUM ZOBI N 253

Voronezh Winter Mathematical School s Dedicated to Selim Krein

m

Selim Grigorievich Krei n

Amer. Math . Soc . Transl . (2) Vol . 184 , 199 8

Introduction

Peter Kuchmen t an d Vladimi r Li n

The task of describing the history of the Voronezh Winter Mathematica l Schoo l and th e rol e o f it s founder , Professo r Seli m Krein , i s both honorabl e an d difficult . Let u s star t wit h som e geography . Voronez h i s a larg e cit y (wit h a populatio n of 1. 2 million ) i n th e Europea n par t o f Russia , clos e t o th e Ukrainia n border . I t has a doze n institution s o f highe r education , includin g th e larg e Voronez h Stat e University. Th e mathematics departmen t a t th e university becam e prominent afte r Mark Krasnoselski i an d Selim Krein joined i t in early 1950' s and began establishin g their mathematica l schools . Th e mai n area s o f interes t i n Voronez h hav e bee n functional analysis , operator theory , partia l differentia l equations , an d topology. I n the fiftie s an d sixtie s th e departmen t becam e a cente r o f activ e researc h i n thes e areas an d attracte d man y brillian t students . On e o f th e greates t feature s o f th e Voronezh mathematica l communit y wa s th e diversit y o f interest s an d willingnes s to explor e ne w areas . However , th e possibilit y o f communicatin g wit h leadin g researchers an d tn e accessibilit y o f mathematica l literatur e wer e severel y limite d in a cit y lik e Voronezh . Apparently , thi s observatio n le d Krei n t o th e ide a o f creating a n annua l conference-typ e even t tha t coul d attrac t leadin g researcher s and woul d allo w loca l mathematician s (especiall y students ) t o lear n abou t ne w trends an d method s i n mathematics . Ther e were , though , som e features tha t wer e intended t o mak e a clea r distinctio n betwee n thi s conferenc e an d th e majorit y o f similar mathematica l gatherings . Firs t o f all , the mai n emphasi s wa s on educatin g local mathematicians throug h lectur e serie s devoted to interesting topics . Thi s ha d several importan t implications . Le t u s lis t som e o f them . Firs t o f all , th e nam e chosen fo r th e gatherin g wa s Voronez h Winte r Mathematica l School , s o i t wa s a "school" rathe r tha n a "conference. " Voronez h mathematician s hav e almos t neve r been invite d t o giv e lectures , sinc e the y wer e availabl e t o student s al l yea r lon g anyway. Lecturer s usually presented a series of lectures rather tha n a single lecture , which enabled them to provide a reasonably understandable introductio n to , and/o r survey o f a subject . Lecturer s wer e asked t o presen t topic s i n such a way that the y could b e understoo d b y a perso n fro m a differen t are a o f mathematics , eve n b y an undergraduat e student . Ther e wer e n o restriction s o n th e are a o f mathematic s presented i n th e lectures . A seriou s effor t wa s mad e t o attrac t a s man y student s

©1998 America n Mathematica l Societ y

ix

x PETE R KUCHMEN T AN D VLADIMI R LI N

as possibl e (includin g undergraduates). 1 Eac h Schoo l wa s planne d t o las t a t leas t a week .

There was a problem, however , wit h attractin g leadin g mathematicians t o suc h a meeting , especiall y o n a yearl y basis . Thi s proble m wa s resolve d b y choosin g a suitable plac e an d time . Th e Schoo l wa s organize d durin g th e winte r brea k i n a tourist resor t i n a beautiful forest , wher e all willing participants had the opportunit y to sk i (cros s country) . Togethe r wit h mathematics , thi s becam e on e o f th e mai n attractions o f the School .

The firs t Schoo l wa s organize d b y S . Krei n i n January-Februar y o f 196 7 an d proved t o be a great success . Sinc e then i t was held each year fo r th e nex t 2 5 years. In th e nineties , althoug h th e Schoo l di d conven e severa l times , an d eve n produce d several offsprin g i n summe r an d winter , it s directio n ha s changed , an d w e will no t discuss th e ne w situation . Th e chang e wa s du e t o severa l factors , amon g the m Krein's retiremen t fro m th e leadershi p o f th e Schoo l an d th e emigratio n o f man y participants. So , whe n talkin g abou t th e Voronez h Winte r Mathematica l School , we mean it s firs t 2 5 years.

Let u s briefl y describ e th e organizatio n o f th e Schoo l an d it s impac t o n th e mathematical communit y o f the forme r Sovie t Union .

The locatio n o f the Schoo l varied sometimes , bu t i t alway s was a tourist resor t in a snow y fores t clos e t o Voronezh . Th e reade r shoul d b e aware , however , tha t the wor d "resort " ha s a meanin g differen t fro m th e on e commo n i n th e Wester n world. On e o f the mos t noticeabl e feature s wa s tha t normall y th e room s wer e ver y poorly heated , whic h on the othe r han d helpe d t o keep the audienc e a t th e lecture s awake. Th e foo d wa s no t o f hig h qualit y either . However , th e qualit y o f lectures , beautiful scenery , an d intensit y o f mathematica l an d socia l communication s mor e than compensate d fo r som e inconveniences .

The Schoo l usuall y laste d fo r 1 0 days , an d normall y worke d accordin g t o th e following schedule . A n earl y breakfas t wa s followe d b y thre e one-hou r lectures . After lunc h ther e wa s som e fre e tim e tha t wa s use d b y man y fo r skiing , b y som e for sleep , an d b y th e mos t zealou s mathematician s fo r discussions . The n on e o r two one-hou r lecture s followed . Som e fre e tim e befor e suppe r wa s als o spen t i n mathematical discussion s an d skiing . Afte r supper , man y paralle l seminar s wit h contributed talk s continue d wel l int o th e evenin g (unti l 9 o r 1 0 p.m.) . An d afte r that "th e rea l lif e started. " Wha t wa s it ? Well , th e lis t i s long : lecture s o n history presente d b y A. Khelemsky , poetr y readings , charade s (i n which V . Arnol d excelled) an d othe r games , plent y o f songs , dance s throug h th e night , an d jus t warm gathering s o f friends (sometime s 2 0 or 3 0 persons i n a tiny room ) tha t coul d continue wel l int o th e nex t morning . Friend s normall y separate d b y thousand s o f miles, whe n the y me t i n th e School , di d no t wan t t o wast e eve n a n hou r withou t communication. A s someon e said , "Th e Schoo l wa s th e mai n benchmar k o f ou r lives. W e lived fro m on e Schoo l t o th e next. "

The Schoo l accepte d abou t 30 0 participants , an d man y friendships , scientifi c careers, an d scientifi c collaboration s starte d there .

The bi g succes s o f the Schoo l wa s i n attractin g brillian t lecturers . W e presen t a lis t o f speaker s (man y o f who m gav e lecture s mor e tha n once) . Unfortunately , we do no t hav e complet e data , s o we ask lecturer s who m w e inadvertently lef t ou t

-'̂ One of th e editor s o f thi s volum e starte d attendin g th e Schoo l a s a sophomore ; som e othe r students starte d a s freshmen .

INTRODUCTION x i

to accep t ou r apologies. So , here are some of the lecturers: V . Arnold, A . Belavin, Yu. Berezanskii , Yu . Daletskii, V . Drinfeld, B . Dubrovin, A . Dynin, A . Fomenko, D. Fuchs, S. Gindikin, E. Gorin, M. Kadec, L. Kantorovich, V . Kharlamov, A. Kho-vanskii, A . Kirillov , S . Kislyakov , M . Krasnoselskii , I . Krichever , P . Kuchment , V. Lin, Yu. Lyubich, G . Margulis, V. Maslov, B . Mityagin, S . Novikov, A. Olevsky, G. Ol'shansky , V . Palamodov , B . Paneah , M . Postnikov , A . Povzner , G . Rosen -blum, S . Samborskii , B . Shabat, V . Shatalov, M . Shubin, M . Solomyak, A . Stern , B. Sternin, A . Varchenko, E. Vinberg, A. Vinogradov, O . Viro, L. Volevich, A. Vol'-pert, M. Zaidenberg, and many other distinguished mathematicians . On e can notice among the lecturers man y Sovie t laureat s o f the most prestigiou s prize s (includin g the Nobel , Fields , and Crafoord Prizes) .

It i s hard t o overestimat e th e impac t o f the Schoo l o n the mathematica l lif e of th e Sovie t Union . Man y undergraduat e an d graduat e student s starte d thei r research career s influence d b y the lectures . Man y peopl e stil l kee p lectur e note s taken there . Th e School provide d a unique opportunit y t o lear n fro m th e leadin g experts abou t development s i n differen t area s o f mathematics . Th e lis t o f theo -retical an d applied area s covere d durin g th e years o f School's operatio n i s so wide that i t almos t coincide s wit h th e Mathematical Subjec t Classificatio n list ! Topic s ranged fro m quantu m group s t o geometry o f Banach spaces , t o fluid dynamics , t o random processes , t o integral geometry , t o K-theory, t o Lie algebras, t o boundar y value problem s fo r PDEs , t o the inverse scatterin g metho d i n nonlinear PDEs , t o classical harmoni c analysis , t o mathematica l method s i n economics , t o tomogra -phy! Man y joint work s and new areas of research starte d i n the School. Beside s its purely scientifi c influence , th e School also played a n important rol e in the personal lives of many of its participants, providin g a warm atmosphere tha t contraste d wit h the norma l wa y of life unde r th e totalitarian Sovie t regime .

This book is a collection of papers writte n b y former lecturer s and participants of th e Voronezh Winte r Mathematica l School . W e think o f it a s a tribut e t o the School and to the 80th birthda y o f Selim Krein , the founder o f the School and one of its main source s o f inspiration .

MATHEMATICS AN D STATISTIC S DEPARTMENT , WICHIT A STAT E UNIVERSITY , WICHITA , K S

67260-0033 E-mail address: kuchment@twsuvm.uc.twsu.ed u

DEPARTMENT O F MATHEMATICS , TECHNION-ISRAE L INSTITUT E O F TECHNOLOGY , 3200 0

HAIFA, ISRAE L

E-mail address: v l in@techunix . t echn ion .ac . i l

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Amer. Math . Soc . Transl . (2) Vol . 184 , 199 8

Selim Grigorievic h Krei n

Peter Kuchmen t

It i s both a privileg e an d a n hono r t o writ e abou t m y teacher , Professo r Seli m Krein, wh o ha s playe d a majo r rol e i n m y life , a s wel l a s i n th e live s o f hundred s of othe r mathematicians . Seli m Krei n ha s a lon g an d distinguishe d caree r a s a researcher an d teacher . Le t m e star t b y describin g hi m a s a teacher . I d o no t know th e exac t figure, bu t th e numbe r o f hi s Ph D student s i s a t leas t eighty . Krein ha s alway s bee n surrounde d b y youn g mathematician s who m h e taugh t an d whose live s h e influence d a lot . H e i s a grea t lecturer . Hi s lecture s an d talk s are alway s wel l prepared , clearl y structured , an d targe t exactl y th e leve l tha t i s appropriate for the audience. I t i s always a pleasure to hear him lecturing. However , the wa y h e teache s explaine s onl y partl y hi s grea t succes s a s a mento r o f youn g researchers. Th e entir e atmospher e i n hi s schoo l i s conduciv e t o creativ e research . Though Krein' s majo r achievement s ar e i n functiona l analysis , operato r theory , partial differentia l equations , differentia l equation s i n Banac h spaces , an d fluid dynamics, h e i s intereste d i n mathematic s a s a whole , rathe r tha n jus t i n certai n areas. I remembe r tha t whe n I wa s a Ph D student , i n hi s seminar s (thoug h the y were designate d t o som e specifi c areas ) w e coul d giv e a tal k o n an y subjec t w e found interesting . Topic s w e worked o n range d fro m severa l comple x variables , t o PDEs, t o non-commutativ e integration , t o K-theory , t o commutativ e algebra , . . . , you nam e it . Th e are a i n whic h a studen t woul d wor k wa s no t necessaril y chose n by Krein . Althoug h h e di d follo w th e standar d procedur e o f assignin g a proble m to a Ph D student , h e allowe d th e bes t o f the m t o choos e th e proble m t o wor k on . The amazin g thin g wa s tha t whe n w e started t o wor k o n a proble m tha t coul d b e very remote from Krein' s curren t interests , he was able to ge t int o the new field and help u s wit h ou r research . T o emphasize freedo m fro m rigi d restriction s o n topics , he called on e of his seminars a t th e Voronezh Winte r Mat h Schoo l the "Semina r o n Higher Mathematics. " I t wa s ver y commo n fo r hi s student s t o organiz e thei r ow n seminars t o stud y som e ne w areas .

Another remarkabl e qualit y o f Krein a s an adviso r i s that h e helps his student s not onl y wit h thei r researc h problems , bu t als o wit h problem s o f everyda y lif e (which often ar e much harder) . Helpin g former student s i n getting decen t jobs an d apartments an d i n overcoming unwritte n restriction s impose d b y the authoritaria n regime wa s quit e commo n fo r him . H e kep t helpin g hi s forme r student s lon g afte r their graduation . I hav e alway s bee n amaze d tha t Krei n remember s th e name s o f thousands o f hi s forme r students .

©1998 America n Mathematica l Societ y

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xiv PETE R KUCHMEN T

Krein's joyfu l character , readines s t o joke , an d abilit y t o char m anybod y ad d to th e admiratio n w e al l fee l towar d him .

Selim Krein ha s always been eager to go an extra mil e to promote mathematic s in Voronezh . H e instigated th e foundin g o f the Mathematic s Researc h Institut e a t Voronezh Stat e University , o f th e Voronez h Mathematica l School , an d o f a serie s of lecture s o n contemporar y topic s i n mathematic s fo r professor s an d graduat e students a t numerou s college s i n Voronezh .

Now le t m e sa y fe w word s abou t o f Krein' s wor k i n mathematics . On e ca n find additiona l informatio n i n paper s writte n o n th e occasio n o f hi s sixtiet h an d seventieth birthday s (Russia n Math . Survey s 4 2 (1987) , no . 5 , 181-183 ; ibid . 3 3 (1978), no . 2 , 215-225). I t i s impossible t o address (eve n skipping details ) al l area s of Krein' s research , s o I wil l concentrat e onl y o n the majo r ones .

Selim Krei n wa s bor n Jul y 15 , 1917 in Odessa . H e received hi s undergraduat e education i n mathematic s a t Kie v Stat e Universit y i n 1935-1940 . Afte r graduat e study i n 1940-1941 , he defended, i n 1942 , his Ph.D. dissertation , writte n unde r th e supervision o f N. N. Bogolyubov. Hi s first affectio n i n mathematic s wa s functiona l analysis, whic h ha s continue d t o b e on e o f hi s majo r area s o f researc h eve r since . His first paper s i n this are a wer e written jointly wit h hi s olde r brothe r Mar k Krei n and hi s teache r Bogolyubov . On e o f th e result s o f hi s dissertatio n wa s a theore m now known a s th e Kreins-Kakutan i theorem .

When Worl d Wa r I I started , Krei n coul d no t g o int o th e Arm y becaus e o f a childhood illnes s tha t ha d damage d on e o f hi s legs . A s a researc h fello w a t th e Mathematics Institut e o f the Ukrainia n Academ y o f Sciences (relocate d t o a regio n not occupie d b y th e Germa n army) , h e starte d t o wor k o n importan t war-relate d projects i n a grou p le d b y M . A . Lavrent'ev . Thi s i s whe n hi s majo r researc h i n fluid dynamic s started . H e was amon g th e first t o introduc e method s o f functiona l analysis t o fluid dynamics . H e ha s studie d th e motio n o f a vesse l partiall y filled with fluid (on e can imagine , fo r instance , a liquid fue l rocket) . Oscillatio n o f a fluid in an ope n vesse l was anothe r topi c t o whic h h e has devote d a lo t o f attention . Al l these investigation s wer e triggered b y importan t applie d problems . Hi s research i n this directio n culminate d i n hi s classified Docto r o f Science s dissertation , whic h h e defended i n 195 0 in th e Mosco w Artiller y Academy , an d i n th e recen t boo k [18]. x

In 1950-1951 Krein headed the Computational Mathematic s Department a t th e Mathematical Institut e o f the Ukrainia n Academ y o f Sciences . Her e h e developed , together wit h M . A . Krasnoselskii , a minima l residua l metho d fo r solvin g system s of linear equations . Computationa l mathematic s becam e on e of the area s t o whic h Krein returne d man y time s durin g hi s career . Severa l o f hi s student s hav e becom e numerical analysts .

After a shor t tim e spen t i n Krivoi Rog , Krein cam e to Voronezh i n 1954 , where he ha s worke d eve r since . Firs t h e wa s Professo r an d Chairma n o f th e Mathe -matics an d Theoretica l Mechanic s Departmen t a t th e Voronez h Forestr y Institut e (currently, Forestr y Academy) . H e became th e Hea d o f the Departmen t o f Partia l Differential Equation s o f Voronez h Stat e Universit y i n 1964 , an d returne d t o hi s previous positio n a t th e Forestr y Institut e i n 1971 . Unde r hi s guidance , th e De -partment o f Partia l Differentia l Equation s o f Voronez h Stat e Universit y an d th e Mathematics an d Theoretica l Mechanic s Departmen t o f the Forestry Institut e hav e become place s o f very activ e mathematica l research .

The number s refe r t o the "Lis t o f Publications b y Seli m Krein" , pp . xvii-xxv i i n this volume .

SELIM GRIGORIEVIC H KREI N x v

Among hi s first studie s i n functiona l analysi s an d functio n theor y wer e work s on singula r integral s ([25—27]) , doubl e operato r integral s ([32 , 36]) , an d hyper -complex system s wit h continua l basi s ([33—35 , 57 , 65]) . Som e o f these area s hav e recently attracte d renewe d attentio n becaus e o f thei r relation s wit h som e contem -porary topic s (se e papers b y Berezanski i an d Daletski i i n thi s volume) . Sinc e the n his activit y i n functiona l analysi s ha s bee n concentrate d mostl y o n th e theor y o f interpolation o f linea r operators , a n are a wit h man y applications , th e mos t impor -tant o f the m i n PDEs . Alon g wit h A.-P . Calderon , J.-L . Lions , J . Peetre , an d E . Gagliardo, Krei n i s one of the founder s o f the contemporar y theor y o f interpolatio n of linear operators . H e introduced th e so-called method o f scales, which has become one of the majo r method s i n this theory . Severa l o f his students hav e become lead -ing expert s i n interpolatio n theory . Th e milestone s o f thi s are a o f Krein' s researc h are the surve y article s an d book s [13 , 16 , 89 , 93 , 155] . Researc h i n fluid dynam -ics an d PDE s le d Seli m Krei n t o anothe r are a o f functiona l analysis , th e stud y o f Fredholm an d semi-Fredhol m operator s an d continuou s o r analyti c familie s o f suc h operators, with the behavior o f spectra an d eigenfunction s o f such operator familie s being th e mai n propert y h e wa s intereste d in . Th e technique s develope d b y Krei n and hi s students i n this area play an important rol e in many pur e an d applie d stud -ies (wav e guide s an d photoni c crystals , amon g th e mos t interestin g ones) . Book s and paper s [7 , 15 , 134 ] reflec t th e result s o f this research . Krei n initiated , edited , and co-authore d a popula r referenc e boo k o n functiona l analysi s (se e it s differen t editions [2 , 4 , 5 , 8 , 9]) .

Problems o f flui d dynamic s le d Krei n t o stud y differentia l equation s i n Ba -nach space s an d semigroup s o f operators . Her e h e als o becam e on e o f th e worl d leaders. Th e book s [3 , 6 ] an d th e surve y articl e [149 ] summariz e result s o n th e well-posedness o f th e Cauch y problem , analyticit y o f solutions , boundar y valu e problems, asymptoti c methods , etc . Man y o f these result s wer e obtaine d b y Krei n and hi s students . I n th e las t tw o decades , Krei n ha s als o worke d o n singularl y perturbed differentia l equation s i n Banac h spaces .

A large part o f Krein's scientific activity has been devoted to various problems of partial differentia l equations . Her e we should mentio n result s o n homeomorphism s created b y ellipti c boundar y valu e problem s [72 , 74] , boundar y valu e problem s for overdetermine d system s o f PDEs , an d boundar y valu e problem s i n variabl e domains. Som e o f these studie s ar e describe d i n hi s book s [10 , 11] .

For more than quarte r o f century, differentia l equation s on Lie groups and man -ifolds hav e attracte d th e attentio n o f Selim Krein . Fo r instance , paper s [109 , 129 , 130, 137 ] treat relation s between infinit e dimensiona l representations o f Lie groups and Cauch y problems for corresponding differentia l equations , differentia l equation s of secon d orde r o n Li e groups , representatio n o f algebra s o f germ s o f differentia l operators wit h analyti c coefficient s b y integro-differentia l operators , constructio n of infinitesima l operator s fo r operator s o f generalize d shift , an d othe r topics . Th e book [14 ] develops analogs o f Floquet theor y fo r equation s o n manifolds . Th e boo k [19] i s devoted t o functio n space s relate d t o representation s o f Li e group s an d Li e algebras. Unfortunately , th e book s [10 , 11 , 14 , 19 ] hav e no t bee n translate d int o English.

Selim Krein is always eager to share his knowledge with others . H e achieves this not onl y throug h hi s brillian t lectures , bu t als o throug h th e textbook s h e writes . The introductor y calculu s boo k [1 ] ha s bee n translate d int o severa l language s ( I do no t kno w exactl y ho w many) . A ver y nic e analysi s textboo k [12 ] treat s man y

xvi PETE R KUCHMEN T

important topic s that ar e usually no t discusse d i n standard textbooks . Selim Krei n also wrot e a n introductor y textboo k [17 ] o n linea r programmin g fo r economic s majors.

Concluding, I would like to say again tha t i t i s an honor fo r m e and many othe r mathematicians t o b e calle d student s o f th e brillian t mathematicia n an d teache r and admirabl e person , Professo r Seli m Krein . W e al l wis h hi m goo d healt h an d a long, productive life .

MATHEMATICS AN D STATISTIC S DEPARTMENT , WICHIT A STAT E UNIVERSITY , WICHITA , K S

67260-0033 E-mail address: kuchment@twsuvm.uc.twsu.ed u

Amer. Math . Soc . Transl . (2) Vol . 184 , 1998

List o f Publications b y Seli m Krei n

Books

1. Krei n S . G. and Ushakov a V . N. , Mathematical Analysis of Elementary Functions, "Fizmat -giz", Moscow , 1963 . (Russian ; Germa n transl. , 1966 ; several othe r transls. )

2. Krei n S . G . (edito r an d coauthor) , Functional Analysis, "Nauka" , Moscow , 1964 . (Russian ; Polish transl. , [4] ; English transls. , [5] , [8]; 2nd ed. , [9] ) MR 32 #153 2

3. Krei n S . G. , Linear Differential Equations in a Banach Space, "Nauka" , Moscow , 1967 . (Russian; Englis h transl. , [6] ) MR 40 #50 8

4. Krei n S . G . (edito r an d coauthor) , Analiza Funkcjonalna, PWN , Warsaw , 1967 . (Polis h transl. o f [2] ) MR 3 6 #3101

5. Krei n S . G . (edito r an d coauthor) , Functional Analysis, Edite d machin e translatio n o f [2], Foreign Technolog y Divisio n MT-65-573 . U.S. Dept. Commerce , Nat . Bur. Standards, Wash -ington, DC ; microfiche, distribute d b y Clearinghous e fo r Federa l Sci . Tech. Inform. , Spring -field, VA , 1968 . MR 38 #256 0

6. Krei n S . G. , Linear Differential Equations in Banach Space, Englis h transl . o f [3] , Transl . Math. Monographs , vol . 29, Amer. Math . Soc , Providence , RI , 1971 . MR 49 #754 8

7. Krei n S . G., Linear Equations in a Banach Space, "Nauka" , Moscow , 1971 . (Russian; trans -lated int o Japanes e i n 1972 ; English transl. , [15] ) MR 5 1 #1114 5

8. Krei n S . G . (edito r an d coauthor) , Functional Analysis, 2n d ed . o f [3] , "Nauka" , Moscow , 1972. (Russian ) M R 5 0 #540 6

9. Krei n S . G . (edito r an d coauthor) , Functional Analysis, Englis h transl . o f [3] , Wolters -Noordhoff, Groningen , 1972 . MR 5 2 #1151

10. Gudovic h I . S . an d Krei n S . G. , Boundary Value Problems for Overdetermined Systems of Partial Differential Equations, Diff . Uravneniy a i Primenen., Trud y Sem . Protsessy Optimal . Upravleniya, Vyp . 9, Ins t Math , an d Phys. . Lithuanian Acad . Sci. , Vilnius, 1974 . (Russian ) MR 5 8 #172 0

11. Ivano v L. , Kotk o L. , an d Krei n S. , Boundary Value Problems in Variable Domains, Diff . Uravneniya i Primenen. , Trud y Sem . Protsess y Optimal . Upravleniya , Vyp . 19 , Inst Math , and Phys . Lithuania n Acad . Sci. , Vilnius, 1977 . (Russian ) M R 5 8 #1750 7

12. Krei n S . G . an d Zobi n N . M. , Mathematical Analysis of Smooth Functions, Voronez h Stat e University, Voronezh , 1978 . (Russian )

13. Krei n S . G., Petunin Yu . I., and Semenov E . M., Interpolation of Linear Operators, "Nauka" , Moscow, 1978 . (Russian ; Englis h transl. , [16] ) MR 81f:4608 6

14. Krei n S . G . an d Yatski n N . I. , Linear Differential Equations on Manifolds, Voronez h Stat e Univ., Voronezh , 1980 . (Russian ) M R 83i:5801 2

15. Krei n S . G. , Linear Equations in Banach Spaces, Englis h transl . o f [7] , Birkhauser, Bosto n MA, 1982 . MR 83m:4701 2

16. Krei n S . G. , Petuni n Yu . I. , and Semeno v E . M. , Interpolation of Linear Operators, Englis h transl. o f [13] , Transl. Math . Monographs , vol . 54, Amer. Math . Soc , Providence , RI , 1982. MR 84j:4610 3

17. Krei n S . G. , Mathematical Programming, Voronez h Stat e Univ. , Voronezh , 1983 . (Russian ) MR 86e:9006 8

18. Kopachevski i N . D. , Krei n S . G. , an d Ng o Zu i Kan , Operator Methods in Linear Hydrody-namics, "Nauka" , Moscow , 1989 . (Russian ) M R 91h:7600 1

©1998 America n Mathematica l Societ y

xvii

:viii LIS T O F PUBLICATION S B Y SELI M KREI N

19. Krei n S . G . an d Pesenso n I . Z. , Spaces of Smooth Elements Generated by the Representation of a Lie Group, Voronez h Stat e Univ. , Voronezh , 1990 . (Russian ) M R 92g:2202 3

Papers

1940. 20. (wit h Krei n M . G.) , On an inner characteristic of the set of all continuous functions defined

on a bicompact Hausdorff space, C . R . (Dokl. ) Acad . Sci . URS S 2 7 (1940) , 427-430 . M R 2 , 222c

1941. 21. (wit h Verniko v I . Kh . an d Tovbi n A . V.) , Sur les anneaux semi-ordonnes, C . R . (Dokl. )

Acad. Sci . URS S 3 0 (1941) , 785-787 . M R 2 , 314 e

1943. 22. (wit h Krei n M . G.) , Sur Vespace des functions continues definies sur un bicompact de Haus-

dorff et ses sous-espaces semi-ordonnes, Mat . Sb . 13(55 ) (1943) , 1-28 . M R 6 , 276 a

1946. 23. (wit h Bogolyubo v N . N.) , On positive absolutely continuous operators, Zh . Inst . Matem .

Akad. Nau k Ukrain . SS R 9 (1946) , 130-139 . (Ukrainian )

1947. 24. (wit h Krasnoselski i M . A.) , On the center of a general dynamical system, Dokl . Akad . Nau k

SSSR 5 8 (1947) , 9-11 . (Russian ) M R 9 , 242 c

1948. 25. (wit h Levi n B . Ya.) , On the convergence of singular integrals, Dokl . Akad . Nau k SSS R 6 0

(1948), 13-16 . (Russian ) M R 10 , 34 e 26. (wit h Levi n B . Ya.) , On the strong representation of functions by singular integrals, Dokl .

Akad. Nau k SSS R 6 0 (1948) , 195-198 . (Russian ) M R 10 , 34 f 27. (wit h Levi n B . Ya.) , On a problem of I. P. Natanson, Uspekh i Mat . Nau k 3 (1948) , no . 3 ,

183-186. (Russian ) M R 10 , 114 a 28. (wit h Korenblu m B . I . an d Levi n B . Ya.) , On certain nonlinear questions of the theory of

singular integrals, Dokl . Akad . Nau k SSS R 6 2 (1948) , 17-20 . (Russian ) M R 10 , 306 f 29. (wit h Ka c G . I.) , On the limit center of a dynamical system, Sb . Trudo v Inst . Matem . Akad .

Nauk Ukrain . SS R (1948) , 121-134 . (Russian )

1949. 30. (wit h Krasnoselski i M . A.) , On a proof of the theorem on category of a projective space,

Ukrain. Mat . Zh . 1 (1949) , no . 2 , 99-102 . (Russian ) M R 14 , 72 h

1950. 31. (wit h Daletski i Yu . L.) , On differential equations in Hilbert space, Ukrain . Mat . Zh . 2 (1950) ,

no. 4 , 71-91 . (Russian ) M R 13 , 954 c 32. (wit h Daletski i Yu . L.) , Some properties of operators depending upon a parameter, Dokl .

Akad. Nau k Ukrain . SS R 6 (1950) , 433-436 . (Ukrainian ) 33. (wit h Berezanski i Yu . M.) , Some classes of continuous algebras, Dokl . Akad . Nau k SSS R 7 2

(1950), 237-240 . (Russian ) M R 12 , 189 a 34. (wit h Berezanski i Yu . M.) , Continuous algebras, Dokl . Akad . Nau k SSS R 7 2 (1950) , 5-8 .

(Russian) M R 12 , 188 f

1951. 35. (wit h Berezanski i Yu . M.) , Hypercomplex systems with a compact basis, Ukrain . Mat . Zh . 3

(1951), 184-204 . (Russian ) M R 14 , 944 d 36. (wit h Daletski i Yu . L.) , Formulas of differentiation with respect to a parameter for functions

of Hermitian operators, Dokl . Akad . Nau k SSS R 7 6 (1951) , 13-16 . (Russian ) M R 12 , 617f

1952. 37. (wit h Krasnoselski i M . A.) , An iteration process with minimal residuals, Mat . Sborni k

31(73) (1952) , 315-334 . (Russian ) M R 14 , 692 d 38. (wit h Krasnoselski i M . A.) , Remark on the distribution of errors in the solution of a system

of linear equations by means of an iterative process, Uspekh i Mat . Nau k 7 (1952) , no . 4(50) , 157-161. (Russian ) M R 14 , 501f

LIST O F PUBLICATION S B Y SELI M KREI N xi x

1953. 39. On functional properties of operators of vector analysis and hydrodynamics, Dokl . Akad .

Nauk SSS R 9 3 (1953) , 969-972 . (Russian ) M R 15 , 906 c 40. Uniform topology in the space of transformations, Mat . Sborni k 33(75 ) (1953) , 627-638 .

(Russian) M R 15 , 547 b 41. On fixed points of a conformal mapping, Uspekh i Mat . Nau k 8 (1953) , no . 1(53) , 155-159 .

(Russian) M R 14 , 742 f

1954. 42. On an indeterminate equation in Hilbert space and its application in potential theory, Us -

pekhi Mat . Nau k 9 (1954) , no . 3(61) , 149-153 . (Russian ) M R 16 , 262 g

1955. 43. (wit h Krasnoselski i M . A.) , On the principle of averaging in nonlinear mechanics, Uspekh i

Mat. Nau k 1 0 (1955) , no . 3(65) , 147-152 . (Russian ) M R 17 , 152 d 44. (wit h Krasnoselski i M . A.) , Nonlocal existence theorems and uniqueness theorems for systems

of ordinary differential equations, Dokl . Akad . Nau k SSS R 10 2 (1955) , 13-16 . (Russian ) M R 17, 151 b

1956. 45. Mathematical problems of the theory of motion of a vessel filled with a fluid, Proc . I l l All -

Union Math . Congress , vol . 1 , Izdat . Akad . Nau k SSSR , Moscow , 1956 , p . 205 . (Russian ) 46. (wit h Krasnoselski i M . A.) , On differential equations in Banach spaces, Proc . I l l All-Unio n

Math. Congress , vol . 2 , Izdat . Akad . Nau k SSSR , Moscow , 1956 , p . 11 . (Russian ) 47. (wit h Krasnoselski i M . A . an d Sobolevski i P . E.) , On differential equations with unbounded

operators in Banach spaces, Dokl . Akad . Nau k SSS R 11 1 (1956) , 19-22 . (Russian ) M R 19 , 550a

48. (wit h Krasnoselski i M . A.), On the theory of ordinary differential equations in Banach spaces, Voronezh. Gos . Univ . Trud y Sem . Punktsional . Anal . 2 (1956) , 3-23 . (Russian ) M R 19 , 140 c

49. (wit h Daletski i Yu . L.) , Integration and differentiation of functions of Hermitian operators and applications to the theory of perturbations, Voronezh . Gos . Univ . Trud y Sem . Funkt -sional. Anal . 1 (1956) , 81-105 ; Englis h transl. , Amer . Math . Soc . Transl . (2 ) 4 7 (1965) , 1-30. M R 18 , 914 d

50. (wit h Krasnoselski i M . A.) , On a class of uniqueness theorems for the equation y' = f(x,y), Uspekhi Mat . Nau k 1 1 (1956) , no . 1(67) , 209-213 . (Russian ) M R 18 , 38 a

1957. 51. On well-posedness classes for certain boundary value problems, Dokl . Akad . Nau k SSS R 11 4

(1957), 1162-1165 . (Russian ) M R 19 , 747 e 52. Differential equations in a Banach space and their application in hydromechanics, Uspekh i

Mat. Nau k 1 2 (1957) , no . 1(73) , 208-211 . (Russian ; Englis h transl. , [64] ) M R 19 , 36 f 53. (wit h Krasnoselski i M . A.) , Continuity conditions for a linear operator in terms of proper-

ties of its square, Voronezh . Gos . Univ . Trud y Sem . Punktsional . Anal . 5 (1957) , 98-101 . (Russian) M R 2 0 #478 4

54. (wit h Prozorovskay a O . I.) , An analogue of Seidel's method for operator equations, Voronezh . Gos. Univ . Trud y Sem . Funktsional . Anal . 5 (1957) , 35-38 . (Russian ) M R 2 0 #208 1

55. (wit h Krasnoselski i M . A . an d Sobolevski i P . E.) , On differential equations with unbounded operators in Hilbert space, Dokl . Akad . Nau k SSS R 11 2 (1957) , 990-993 . (Russian ) M R 19 , 747b

56. (wit h Moisee v N . N.) , On oscillations of a vessel containing a liquid with a free surface, Prikl. Mat . Mekh . 2 1 (1957) , 169-174 . (Russian ) M R 19 , 695 g

57. (wit h Berezanski i Yu . M.) , Hypercomplex systems with continual basis, Uspekh i Mat . Nau k 12 (1957) , no . 1(73) , 147-152 . (Russian ; Englis h transl. , [65] ) M R 19 , 154 d

58. (wit h Krasnoselski i M . A . an d Myshki s A . D.) , An extended session in March 1957 of the Voronezh Seminar on Functional Analysis, Uspekh i Mat . Nau k 1 2 (1957) , no . 4 , 241-250 . (Russian)

1958. 59. (wit h Glushk o V . P.) , Fractional powers of differential operators and imbedding theorems,

Doklady Akad . Nau k SSS R 12 2 (1958) , 963-966 . (Russian ) M R 2 0 #657 8

:x LIS T O F PUBLICATION S B Y SELI M KREI N

60. (wit h Sobolevski i P . E.) , A differential equation with an abstract elliptical operator in Hilbert space, Dokl . Akad . Nau k SSS R 11 8 (1958) , 233-236 . (Russian ) M R 2 0 #604 3

61. (wit h Krasnoselski i M . A.) , On differential equations in a Banach space, Proc . Il l Ail-Unio n Math. Congress , vol . 3 , Izdat . Akad . Nau k SSSR , Moscow , 1958 , pp . 73-80 . (Russian )

1960. 62. On an interpolation theorem in operator theory, Dokl . Akad . Nau k SSS R 13 0 (1960) , 4 9 1 -

494; Englis h transl. , Sovie t Math . Dokl . 1 (1960) , 61-64 . M R 2 2 #986 0 63. On the concept of a normal scale of spaces, Dokl . Akad . Nau k SSS R 13 2 (1960) , 510-513 ;

English transl , Sovie t Math . Dokl . 1 (1960) , 586-589 . M R 2 2 #1236 1 64. Differential equations in Banach space and their application in hydrodynamics, Amer . Math .

Soc. Transl . (2 ) 1 6 (1960) , 423-426 . (Englis h transl . o f [52] ) M R 2 2 #823 1 65. (wit h Berezanski i Yu . M.) , Hypercomplex systems with continuous basis, Amer . Math . Soc .

Transl. (2 ) 1 6 (1960) , 358-364 . (Englis h transl . o f [57] ) M R 2 2 #836 8 66. (wit h Prozorovskay a O . I.) , Analytic semi-groups and ill-posed problems for evolutionary

equations, Dokl . Akad . Nau k SSS R 13 3 (1960) , 277-280 ; Englis h transl. , Sovie t Math . Dokl . 1 (1960) , 841-844 . M R 2 7 #184 5

67. (wit h Glushk o V . P.) , Inequalities for norms of derivatives in weighted L p-spaces, Sibirsk . Mat. Zh . 1 (1960) , 343-382 ; Englis h transl. , Amer . Math . Soc . Transl . (2 ) 8 5 (1969) , 1-50 . MR 2 4 #A350 7

1961. 68. Ill-posed problems and estimates of solutions of parabolic equations, Ill-pose d Problem s o f

Mathematics an d Mechanics , Sibirsk . Otdel . Akad . Nau k SSSR , Novosibirsk , 1961 , pp. 84-86 . (Russian)

69. (wit h Petuni n Yu . I.) , A relationship criterion for two Banach spaces, Dokl . Akad . Nau k SSSR 13 9 (1961) , 1295-1298 ; Englis h transl. , Sovie t Math . Dokl . 2 (1961) , 1080-1083 . M R 25 #537 0

70. (wit h Semeno v E . M.) , A scale of spaces, Dokl . Akad . Nau k SSS R 13 8 (1961) , 763-766 ; English transl. , Sovie t Math . Dokl . 2 (1961) , 706-710 . M R 2 5 #435 2

1962. 71. (wit h Lapte v G . I.) , Boundary-value problems for an equation in Hilbert space, Dokl . Akad .

Nauk SSS R 14 6 (1962) , 535-538 ; Sovie t Math . Dokl . 3 (1962) , 1350-1354 . M R 2 7 #600 0

1963. 72. (wit h Berezanski i Yu . M . an d Roitber g Ya . A.) , A theorem on homeomorphisms and local

increase of smoothness up to the boundary for solutions of elliptic equations, Outline s Join t Soviet-American Sympos . Partia l Differentia l Equation s (Novosibirsk , 1963) , Sibirsk . Otdel . Akad. Nau k SSSR , Moscow , pp . 33-38 . M R 3 5 #56 2

73. (wit h Prozorovskay a O . L) , Approximate methods of solving ill-posed problems, Zh . Vychisl . Mat. i Mat . Fiz . 3 (1963) , 120-130 ; Englis h transl. , USS R Comput . Math , an d Math . Phys . 3 (1963) , 153-167 . M R 2 7 #309 4

74. (wit h Berezanski i Yu . M . an d Roitber g Ya . A.) , A theorem on homeomorphisms and local increase of smoothness up to the boundary for solutions of elliptic equations, Dokl . Akad . Nauk SSS R 14 8 (1963) , 745-748 ; Englis h transl. , Sovie t Math . Dokl . 4 (1963) , 152-155 . M R 26 #403 0

1964. 75. Oscillations of a viscous fluid in a container, Dokl . Akad . Nau k SSS R 15 9 (1964) , 262-265 ;

English transl. , Sovie t Math . Dokl . 5 (1964) , 1467-1471 . M R 3 1 #646 1 76. Interpolation theorems in operator theory, and embedding theorems, Proc . Fourt h Ail-Unio n

Math. Congr . (Leningrad , 1961) , Vol . II , "Nauka" , Leningrad , 1964 , pp . 504-510 . (Russian ) MR 3 6 #314 4

77. (wit h Krasnoselski i M . A.) , Operator equations in function spaces, Proc . Fourt h All-Unio n Math. Congr . (Leningrad , 1961) , Vol . II , "Nauka" , Leningrad , 1964 , pp . 292-299 . (Russian ) MR 3 6 #292 6

78. (wit h Petuni n Yu . I.) , On the concept of minimal scale of spaces, Dokl . Akad . Nau k SSS R 154 (1964) , 30-33 ; Englis h transl. , Sovie t Math . Doklad y 5 (1964) , 24-27 . M R 2 8 #433 4

LIST O F PUBLICATION S B Y SELI M KREI N xx i

79. (wit h Askerov N . G. an d Lapte v G . I.) , On a class of nons elf adjoint boundary-value problems, Dokl. Akad . Nau k SSS R 15 5 (1964) , 499-502 ; Englis h transl. , Sovie t Math . Dokl . 5 (1964) , 424-427. M R 2 8 #334 7

80. (wit h Lapte v G . I.) , Boundary value problems with a parameter in the boundary condi-tion, Proc . 3r d All-Unio n Sympos . Diffractio n an d Wav e Theory , Tbilisi , 1964 , pp . 39-41 . (Russian)

81. (wit h Krasnoselski i M . A. , Rutitski i Ya . B. , an d Sobole v V . I.) , On mathematical life in Voronezh, Uspekh i Mat . Nau k 1 9 (1964) , no . 3 , 225-245 . (Russian )

1965. 82. (wit h Simono v A . S.) , Theorem on homomorphisms and quasilinear equations, All-Unio n

Conf. Application s o f Functiona l Analysi s an d Nonlinea r Problems . Abstract s o f Reports , Akad. Nau k Azerb . SSR , Baku , 1965 , pp . 62-63 . (Russian )

1966. 83. Well-posedness of the Cauchy problem and analyticity of solutions of the evolution equation,

Dokl. Akad . Nau k SSS R 17 1 (1966) , 1033-1036 ; Englis h transl. , Sovie t Math . Dokl . 7 (1966) , 1594-1598. M R 3 4 #792 5

84. (wit h Petuni n Yu . I . an d Semeno v E . M.) , Hyperscales of Banach lattices, Dokl . Akad . Nau k SSSR 17 0 (1966) , 265-267 ; Englis h transl. , Sovie t Math . Dokl . 7 (1966) , 1185-1188 . M R 3 4 #3299

85. (wit h Lapte v G . I.) , Boundary value problems for second order differential equations in a Banach space. I , Differentsial'ny e Uravneniy a 2 (1966) , 382-390 ; Englis h transl. , Differentia l Equations 2 (1966) , 189-194 . M R 3 3 #766 2

86. (wit h Lapte v G . I.) , Well-posedness of boundary value problems for a differential equation of the second order in a Banach space. II , Differentsial'ny e Uravneniy a 2 (1966) , 919-926 ; English transl. , Differentia l Equation s 2 (1966) , 478-481 . M R 3 4 #304 9

87. (wit h Shablitskay a L . N.) , Stability of difference schemes for the Cauchy problem, Zh . Vy -chisl. Mat . i Mat . Fiz . 6 (1966) , 648-664 ; Englis h transl. , USS R Comput . Math , an d Math . Phys. 6 (1966) , no . 4 , 54-73 . M R 3 3 #811 8

88. (wit h Simono v A . S.) , A theorem of homeomorphisms and quasilinear equations, Dokl . Akad . Nauk SSS R 16 7 (1966) , 1226-1229 ; Englis h transl. , Sovie t Math . Dokl . 7 (1966) , 551-554 . MR 3 3 #613 8

89. (wit h Petuni n Yu . I.) , Scales of Banach spaces, Uspekh i Mat . Nau k 2 1 (1966) , no . 2 (128) , 89-168; Englis h transl. , Russia n Math . Survey s 2 1 (1966) , no . 2 , 85-159 . M R 3 3 #171 9

90. (wit h Glushk o V . P . an d Mukhi n V . E.) , On global and local optimal plans in problems of linear programming with two-sided bounds, Optima l Programmin g i n Industria l Problems , vol. 2 , Voronezh . Gos . Univ. , Voronezh , 1966 , pp . 89-90 . (Russian )

91. (wit h Ievlev a O . B.) , On oscillations of a viscous fluid in a vessel, Abstract s Internat . Congr . Math., Sect . 12 , Moscow , 1966 , p . 37 .

92. (wit h Petuni n Yu . I.) , New results in the theory of scales of Banach spaces, Abstract s Inter -nat. Congr . Math. , Sect . 5 , Moscow , 1966 , p . 56 .

1967. 93. (wit h Petuni n Yu . I . an d Semeno v E . M.) , Scales of Banach lattices of measurable functions,

Trudy Moskov . Mat . Obshch . 1 7 (1967) , 293-322 ; Englis h transl. , Trans . Mosco w Math . Soc . 17 (1967) , 323-353 . M R 3 6 #692 5

94. Sixth joint conference in physics and mathematics of the Far East, Uspekh i Mat . Nau k 2 2 (1967), no . 1 , 197-198 . (Russian )

95. First Voronezh Winter Mathematical School, Uspekh i Mat . Nau k 2 2 (1967) , no . 4 , 189-190 . (Russian)

1968. 96. On oscillations of a viscous fluid and related operator equations, Funktsional . Anal , i Prilo -

zhen. 2 (1968) , no . 2 , 40-50 . (Russian ) 97. The behavior of solutions of elliptic problems under variation of the domain, Studi a Math .

31 (1968) , 411-424 . (Russian ) M R 3 8 #358 6 98. The behavior of solutions of elliptic problems under variation of the domain, Proc . 7t h Math .

Phys. Conf . Fa r East, , Khabarovsk , 1968 , p . 18 . (Russian ) 99. Linear equations in Banach space, Lectur e Notes , Voronez h Stat e Univ. , Voronezh , 1968 , 6 9

pp. (Russian ) M R 5 1 #1114 6

xxii LIS T O F PUBLICATION S B Y SELI M KREI N

100. (wit h Lapte v G . I.) , On the problem of the motion of a viscous fluid in an open vessel, Funktsional. Anal , i Prilozhen . 2 (1968) , no . 1 , 40-50 ; Englis h transl. , Funct . Anal . Appl . 2 (1968), 38-47 . M R 4 0 #171 4

101. (wit h Askero v N . K . an d Lapte v G . I.) , The problem of the oscillations of a viscous liquid and the operator equations connected with it, Funktsional . Anal , i Prilozhen. 2 (1968) , no . 2 , 21-31; Englis h transl. , Funct . Anal . Appl . 2 (1968) , 115-124 . M R 3 8 #55 9

102. (wit h Glushk o V. P.) , Degenerate linear differential equations in a Banach space, Dokl . Akad . Nauk SSS R 18 1 (1968) , 784-787 ; Englis h transl. , Sovie t Math . Dokl . 9 (1968) , 919-922 . M R 38 #39 3

1969. 103. (wit h Kuliko v I . M.) , The Maxwell-Leontovich operator, DifferentsiaKny e Uravneniy a 5

(1969), 1275-1282 ; Englis h transl. , Differentia l Equation s 5 (1969) , 937-943 . M R 4 2 #90 0 104. (wit h Trofimo v V . P.) , Holomorphic operator-valued functions of several complex variables,

Funktsional. Anal , i Prilozhen . 3 (1969) , no . 4 , 85-86 ; Englis h transl. , Funct . Anal . Appl . 3 (1969), 330-331 . M R 4 1 #746 6

105. (wit h Ng o Zu i Kan) , The problem of small motions of a body with a cavity partially filled with a viscous fluid, Prikl . Mat . Mekh . 3 3 (1969) , 117-123 ; Englis h transl. , J . Appl . Math . Mech. 3 3 (1969) , 110-117 . M R 4 1 #489 7

106. (wit h Ng o Zu i Kan) , Asymptotic method in the problem of oscillations of a strongly viscous fluid, Prikl . Mat . Mekh . 3 3 (1969) , 456-464; Englis h transl. , J . Appl . Math . Mech . 3 3 (1969) , 442-450. M R 4 1 #389 9

107. (wit h Lapte v G . I.) , An abstract scheme for the examination of parabolic problems in non-cylindrical regions, Differentsial /nye Uravneniy a 5 (1969) , 1458-1469 ; Englis h transl. , Differ -ential Equation s 5 (1969) , 1073-1081 . M R 4 1 #64 9

108. 77 7 Voronezh Winter Mathematical School, January 26 - February 6 1969, Uspekh i Mat . Nauk 2 4 (1969) , no . 4 , 230-231 . (Russian )

1970. 109. (wit h Shikhvato v A . M.) , Linear differential equations on a Lie group, Funktsional . Anal , i

Prilozhen. 4 (1970) , no . 1 , 52-61 ; Englis h transl. , Funct . Anal . Appl . 4 (1970) , 46-54 . M R 55 #1286 8

110. (wit h Trofimo v V . P.) , Noetherian operators that depend holomorphically on parameters, Function Space s an d Operato r Equation s (Proc . Sem . Functiona l Anal. , Math . Dept. , Voro -nezh Stat e Univ. , Voronezh , 1970) , Voronez h Stat e Univ. , Voronezh , 1970 , pp . 63-85 . (Rus -sian) M R 5 5 #383 9

111. (wit h Trofimo v V . P.) , The multiplicity of a characteristic point of a holomorphic operator-function, Mat . Issled . 5 (1970) , no . 4(18) , 105-114 . (Russian ) M R 4 7 #86 7

112. (wit h Savchenk o Yu . B.) , Exponential dichotomy for partial differential equations, Differen -tsiarnye Uravneniy a 8 (1972) , 835-844 ; Englis h transl. , Differentia l Equation s 8 (1972) , 635-642. M R 4 6 #394 1

113. (wit h Osipo v V . B.) , Lyapunov functions and Cauchy problems for certain systems of partial differential equations, Differentsial'ny e Uravneniy a 6 (1970) , 2053-2061 ; Englis h transl. , Differential Equation s 6 (1970) , 1560-1565 . M R 4 5 #897 8

114. (wit h Petuni n Yu . I . an d Semeno v E . M.) , Imbedding theorems and interpolation of lin-ear operators, Imbeddin g Theorem s an d Thei r Application s (Proc . Sympos. , Baku , 1966) , "Nauka", Moscow , 1970 , pp . 127-131 , 245 . (Russian ) M R 4 7 #234 2

115. (wit h Lapte v G . I . an d Tsvetkov a G . A.) , The Hadamard well-posedness of the Cauchy problem for an evolution equation, Dokl . Akad . Nau k SSS R 19 2 (1970) , 980-983 ; Englis h transl., Sovie t Math . Dokl . 1 1 (1970) , 763-766 . M R 4 2 #63 7

116. Voronezh Winter Mathematical School, January 26-February 31, 1970, Uspekh i Mat . Nau k 25 (1970) , no . 5 , 265-266 . (Russian )

1971. 117. (wit h Kuchmen t P . A.) , A certain approach to the interpolation problem for linear operators,

Voronezh. Gos . Univ . Trud y Nauchno-Issled . Inst . Mat . VG U 3 (1971) , 54-60 . (Russian ) M R 50 #810 6

118. Interpolation of linear operators, and properties of the solutions of elliptic equations, El -liptische Differentialgleichungen , Ban d II , Schriftenreih e Inst . Math . Deutsch . Akad . Wiss .

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Berlin, Reih e A , Hef t 8 , Akademie-Verlag , Berlin , 1971 , pp . 155-166 . (Russian ) M R 4 9 #9385

119. (wit h Gudovic h I . S.) , Certain boundary value problems that are elliptic in a subspace, Mat . Sbornik 84(126 ) (1971) , 595-606 ; Englis h transl. , Math . USS R Sb . 1 3 (1971) , 589-601 . M R 43 #776 4

120. Fifth Voronezh Winter Mathematical School, Uspekh i Mat . Nau k 2 6 (1971) , no . 5 , 270-272 . (Russian)

1972. 121. (wit h Yatski n N . I.) , Differential form equations, Voronezh . Gos . Univ . Trud y Nauchno -

Issled. Inst . Mat . VG U 5 (1972) , 75-79 . (Russian ) M R 5 6 #669 1 122. (wit h Gudovic h I . S.) , Boundary value problems for operators of exterior differentiation,

Voronezh. Gos . Univ . Trud y Nauchno-Issled . Inst . Mat . VG U 5 (1972) , 35-45 . (Russian ) MR 5 6 #669 0

123. (wit h Semeno v E . M.) , A certain property of equimeasurable functions, Voronezh . Gos . Univ . Trudy Nauchno-Issled . Inst . Mat . VG U 5 (1972) , 70-74 . (Russian ) M R 5 6 #582 3

124. (wit h Gudovic h I . S.) , Elliptic boundary value problems for the system I ° J u — / , Funk -\diJ

tsional. Anal , i Prilozhen. 6 (1972) , no . 4, 75-76 ; English transl. , Funct . Anal . Appl . 6 (1972) , 313-319. M R 4 7 #721 3

125. (wit h Gudovic h I . S . and Kuliko v I . M.) , Boundary value problems for the Maxwell equations, Dokl. Akad . Nau k SSS R 20 7 (1972) , 321-324 ; Englis h transl. , Sovie t Phys . Dokl . 1 7 (1972) , 1053-1055. M R 4 7 #544 0

126. (wit h Borisovic h Yu . G.) , VI Voronezh Winter Mathematical School, Uspekh i Mat . Nau k 2 7 (1972), no . 5 , 273-275 . (Russian )

127. (wit h Savchenk o Yu . B.) , On the exponential dichotomy for partial differential equations, Differentsial'nye Uravnenij a 8 (1972) , 835-844 ; Englis h transl. , Differentia l Equation s 8 (1972), 635-642. . M R 4 6 #394 1

1973. 128. (wit h L'vi n S . Ya.) , A general initial problem for a differential equation in a Banach space,

Dokl. Akad . Nau k SSS R 21 1 (1973) , 530-533 ; English t rans l , Sovie t Math . Dokl . 1 4 (1973) , 1058-1062. M R 4 9 #754 9

129. (wit h Grabovskay a R . Ya.) , A certain representation of the algebra of differential operators, and the differential equations connected with it, Dokl . Akad . Nau k SSS R 21 2 (1973) , 280 -283; Englis h transl. , Sovie t Math . Dokl . 1 4 (1973) , 1346-1350 . M R 4 9 #763 3

130. (wit h Grabovskay a R . Ya.) , The formula for the permutation of functions of operators that represent a Lie algebra, Funktsional . Anal , i Prilozhen . 7 (1973) , no . 3 , 81 ; English transl. , Funct. Anal . Appl . 7 (1973) , 236-237 . M R 4 9 #118 0

131. (wit h Sablitskay a L . N.) , Necessary conditions for the stability of difference schemes, and the eigenvalues of difference operators, Zh . Vychisl . Mat . i Mat . Fiz . 1 3 (1973) , 647-657 ; English transl. , USS R Comput . Math , an d Math . Phys . 1 3 (1973) , no . 3 , 138-151 . M R 4 8 #10137

132. (wit h Semeno v E . M.) , Interpolation of operators of weakened type, Funktsional . Anal , i Prilozhen. 7 (1973) , no . 2 , 89-90 ; Englis h transl. , Funct . Anal . Appl . 7 (1973) , 161-162 . M R 47 #397 8

1974. 133. (wit h Efimo v N . V. , Kantorovic h L . V. , Iokhvido v I . S. , Krasnoselski i M . A. , an d Lyusterni k

L. A.) , Vladimir Ivanovich Sobolev (on the occasion of his sixtieth birthday), Uspekh i Mat . Nauk 2 9 (1974) , no . 1 , 247-250 ; Englis h transl. , Russia n Math . Survey s 2 9 (1974) , no . 1 , 157-160. M R 5 2 #779 8

1975. 134. (wit h Zaidenber g M . G. , Kuchmen t P . A. , an d Panko v A . A.) , Banach bundles and linear

operators, Uspekh i Mat . Nau k 3 0 (1975) , no . 5 , 101-157 ; Englis h transl. , Russia n Math . Surveys 3 0 (1975) , no . 5 , 115-175 . M R 5 4 #374 1

135. (wit h Kotk o L . A.) , The completeness of a system of eigen- and associated functions of boundary value problems with a parameter in the boundary conditions, Collectio n o f Article s on Application s o f Functiona l Analysis , Voronezh . Tekhnolog . Inst. , Voronezh , 1975 , pp. 7 1 -89. (Russian ) M R 5 8 #173 0

xxiv LIS T O F PUBLICATION S B Y SELI M KREI N

1976. 136. (wit h Semeno v E . M.) , Some interpolation theorems of the theory of linear operators and

their applications, Imbeddin g Theorem s an d Thei r Application s (Proc . All-Unio n Sympos. , Alma-Ata, 1973) , "Nauka " Kazah . SSR , Alma-Ata , 1976 , pp. 64-68 . (Russian ) M R 5 8 #221 3

137. (wit h Grabovskay a R . Ya.) , Second order differential equations with operators generating a Lie algebra representation, Math . Nachr . 7 5 (1976) , 9-29 . M R 5 8 #177 3

138. (wit h Kotk o L . A.) , The completeness of the system of eigen- and associated functions of boundary value problems with a parameter in the boundary conditions, Dokl . Akad . Nau k SSSR 22 7 (1976) , 288-290 ; Englis h transl. , Sovie t Math . Dokl . 1 7 (1976) , 390-393 . M R 5 3 #6117

1977. 139. Interpolation of linear operators in spaces of smooth functions, Operato r Theor y i n Func -

tion Space s (Proc . School , Novosibirsk , 1975) , "Nauka" , Novosibirsk , 1977 , pp . 188-205 . (Russian) M R 5 8 #211 4

140. (wit h Dmitrie v V . I . an d Ovchinniko v V . I.) , Fundamentals of the theory of interpolation of linear operators, Geometr y o f Linea r Space s an d Operato r Theory , Yaroslav . Gos . Univ. , Yaroslavl, 1977 , pp . 31-74 . (Russian ) M R 5 8 #3033 6

1978. 141. (wit h Furmenk o A . I.) , Dynamic equivalence of linear differential operators with nilpotent

operators, Approximat e Method s i n Differentia l Equation s an d Thei r Applications , vol . 4 , Kuybyshev. Gos . Univ. , Kuybyshev , 1978 , pp . 47-56 . (Russian ) M R 83g:3404 3

142. (wit h Dmitrie v V . I.) , Interpolation of operators of weak type, Anal . Math . 4 (1978) , 83—99. MR 80h:4603 6

1980. 143. (wit h Polichk a N . P.) , Behavior of the solutions of boundary value problems for the Lavren-

t' ev-Bitsadze equation under variation of the domain, Partia l Differentia l Equation s (Proc . Conf., Novosibirsk , 1978) , "Nauka" , Novosibirsk , 1980 , pp . 39-41 , 247 . (Russian ) M R 82h:35071

144. (wit h Nikolov a L . I.) , Holomorphic functions in a family of Banach spaces, and interpolation, Dokl. Akad . Nau k SSS R 25 0 (1980) , 547-550 ; Englis h transl. , Sovie t Math . Dokl . 2 1 (1980) , 131-134. M R 81j:4611 2

1981. 145. (wit h Chernysho v K . I.) , Analogue of Tikhonov's theorem for the equation (A+eB)x — C{t)x,

Approximate Method s i n Differentia l Equation s an d Thei r Applications , Kuybyshev . Gos . Univ., Kuybyshev , 1981 , pp. 103-115 . (Russian ) M R 84m:3408 6

146. (wit h Chernysho v K . I.) , Behavior of solutions of general linear systems depending mero-morphically on a small parameter, Dokl . Akad . Nau k SSS R 26 0 (1981) , 530-535 ; Englis h transl., Sovie t Math . Dokl . 2 4 (1981) , 297-302 . M R 84c:3408 4

147. (wit h Kurin a G . A.) , Singular perturbations in problems of optimal control, Stabilit y o f Motion. Analytica l Mechanics . Contro l o f Motion , "Nauka" , Moscow , 1981 , pp . 170-178 ; English transl. , Amer . Math . Soc . Transl . (2 ) 12 7 (1986) , 33-41 . M R 83j:4902 0

1982. 148. (wit h Nikolov a L . I.) , A complex interpolation method for a family of Banach spaces, Ukrain .

Mat. Zh . 3 4 (1982) , 31-42 ; Englis h transl. , Ukrainia n Math . J . 3 4 (1982) , 26-36 . M R 84a:46162

1983. 149. (wit h Khaza n M . I.) , Differential equations in a Banach space, Itog i Nauk i i Tekhniki .

Matem. Anal. , vol . 21 , VINITI, Moscow , 1983 , pp. 130-264 ; Englis h transl. , J . Sovie t Math . 30 (1985) , 2154-2239 . M R 85f:3411 6

1984. 150. (wit h Nikolov a L . Y.) , On the method of complex interpolation, Comple x Analysi s an d Ap -

plications '8 1 (Varna , 1981) , Bulgar . Acad . Sci. , Sofia , 1984 , pp . 298-300 . M R 88a:4608 8 151. (wit h Polichk a N . P.) , A priori estimates for solutions of a problem with displacement for the

Lavrent' ev-Bitsadze equation, Differentsial'ny e Uravneniy a 2 0 (1984) , 2112—2120 ; Englis h transl., Differentia l Equation s 2 0 (1984) , 1492-1498 . M R 86f:3512 8

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152. (wit h Levi n V . I . an d Simono v A . S.) , L. M. Likhtarnikov (on the occasion of his sixtieth birthday), Mat . v Shkol e (1984) , no . 3 , 77 . (Russian ) M R 85m:0107 3

153. (wit h Chernysho v K . I.) , Singularly perturbed differential equations in a Banach space, Nint h Internat. Conf . Nonlinea r Oscillation s (Kiev , 1981) , vol . 1 , "Naukov a Dumka" , Kiev , 1984 , pp. 193-197 . (Russian )

1985. 154. Singularly perturbed linear differential equations in a Banach space, Differentsial'ny e Urav -

neniya 2 1 (1985) , 1814-1817 . (Russian ) M R 87a:3400 1

1986. 155. (wit h Brudny i Yu . A . an d Semeno v E . M.) , Interpolation of linear operators, Itog i Nauk i i

Tekhniki. Matem . Anal. , vol . 24 , VINITI, Moscow , 1986 , pp. 3-163 ; Englis h transl. , J . Sovie t Math. 4 2 (1988) , 2009-2112 . M R 88e:4605 6

156. Asymptotic decomposition of operator equations, Lyapuno v Function s an d Thei r Applica -tions, "Nauka" , Novosibirsk , 1986 , pp . 206-214 . (Russian ) M R 88e:3410 4

1987. 157. (wit h L'vi n S . Ya.) , Overdetermined and underdetermined equations in Hilbert spaces, Izv .

Vyssh. Uchebn . Zaved . Mat . 1987 , no . 9 , 59-66 ; Englis h t rans l , Sovie t Math . (Iz . VUZ ) 3 1 (1987), no . 9 , 71-80 . M R 89d:4701 9

158. (wit h Berezanski i Yu . M. , Gelfan d I . M. , Krei n M . G. , Mitropol'ski i Yu . A. , an d Skorokho d A. V.) , Yurii L'vovich Daletskii (on the occasion of his sixtieth birthday), Uspekh i Mat . Nauk 4 2 (1987) , no . 4(256) , 213-214 ; Englis h transl. , Russia n Math . Survey s 4 2 (1987) , no. 4 , 183-185 . M R 89h:0103 8

159. (wit h L'vi n S . Ya.), Overdetermined and underdetermined elliptic problems, Functiona l Anal -ysis an d Mathematica l Physics , Akad . Nau k SSS R Sibirsk . Otdel. , Inst . Mat. , Novosibirsk , 1985, pp . 106-116 . (Russian ) M R 88h:3503 7

1988. 160. (wit h Polichka N. P.), Stability of solutions of a problem with shift for the Lavrent' ev-Bitsadze

equation with variation of the domain, Applie d Problem s i n Statistica l Analysis , Akad . Nau k SSSR, Sibirsk . Otdel. , Dal'nevostochn . Fil. , Vladivostok , 1988 , pp . 16-29 . (Russian ) M R 91k:35176

161. (wit h L'vi n S . Ya.) , Partially overdetermined and underdetermined elliptic problems, Izv . Vyssh. Uchebn . Zaved . Mat . 1988 , no . 10 , 15-23 ; Englis h transl. , Sovie t Math . (Iz . VUZ ) 32 (1988) , no . 10 , 19-30 . M R 90d:3521 3

162. (wit h L'vi n S . Ya.) , Underdetermined boundary value problems, Functio n Space s an d Equa -tions o f Mathematica l Physics , Voronez h Stat e Univ. , Voronezh , 1988 , pp . 17-24 . (Russian ) MR 90a:3517 1

163. (wit h L'vi n S . Ya.) , An approximation approach to overdetermined and underdetermined boundary value problems, Functiona l an d Numerica l Method s i n Mathematica l Physics , "Naukova Dumka" , Kiev , 1988 , pp . 113-117 . (Russian )

1989. 164. (wit h Kopachevski i N . D.) , A problem of the flow of a viscous fluid, Z . Anal . Anwendunge n

8 (1989) , 557-561 . (Russian ) M R 91f:7601 8 165. An abstract scheme for the consideration of boundary value problems, Applicatio n o f Ne w

Methods o f Analysis t o Differentia l Equations , Voronez h Stat e Univ. , Voronezh , 1989 , pp. 46 -51. (Russian ) M R 91c:4702 1

166. (wit h L'vi n S . Ya.) , Solution of overdetermined and underdetermined elliptic problems in the case of nonsmooth data, Ukrain . Mat . Zh . 4 1 (1989) , 1222-1225 ; Englis h transl. , Ukrainia n Math. J . 4 1 (1989) , 1053-1056 . M R 91b:3508 0

167. (wit h Cha n Tkh u Kha) , The problem of the flow of a nonuniformly heated viscous fluid, Zh . Vychisl. Mat . i Mat . Fiz . 2 9 (1989) , 1153-1158 ; Englis h transl. , USS R Comput . Math , an d Math. Phys . 2 9 (1989) , no . 4 , 127-131 . M R 90m:3515 4

1990. 168. (wit h Fomi n V . I.) , Small perturbations of singular differential equations with unbounded

operator coefficients, Dokl . Akad . Nau k SSS R 31 4 (1990) , 77-79 ; Englis h transl. , Sovie t Math. Dokl . 4 2 (1991) , 313-315 . M R 92e:3407 6

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169. (wit h Tovbi s A . I.) , Linear singular differential equations in finite-dimensional and Banach spaces, Algebr a i Analiz 2 (1990) , no . 5 , 1-62 ; Englis h transl. , Leningra d Math . J . 2 (1991) , 931-985. M R 92e:3400 3

170. (wit h Utochkin a E . O.) , An implicit canonical equation in a Hilbert space, Ukrain . Mat . Zh . 42 (1990) , 388-390 ; Englis h transl. , Ukrainia n Math . J . 4 2 (1990) , 345-347 . M R 91d:3406 2

1991. 171. (wit h Birma n M . Sh. , Ladyzhenskay a O . A. , Rozenblyu m G . V. , an d Safaro v Yu . G.) , Mikhail

Zakharovich Solomyak (on the occasion of his sixtieth birthday), Uspekh i Mat . Nau k 4 6 (1991), no . 4(280) , 183-184 ; Englis h transl. , Russia n Math . Survey s 4 6 (1991) , no . 4 , 217 -219. M R 92k:0102 5

172. (wit h Vasil'e v V . V. an d Piskare v S . I.) , Operator semigroups, cosine operator functions, and linear differential equations, Itog i Nauk i i Tekhniki, Matem . Anal. , vol . 28 , VINITI, Moscow , 1990, pp . 87-202 ; Englis h transl. , J . Sovie t Math . 5 4 (1991) , 1042-1129 . M R 91k:4709 4

1994. 173. (wit h Belyaev a E . V.) , Homogeneous Volterra operator equations with a regular singularity,

Russian J . Math . Phys . 2 (1994) , 3-12 . M R 95h:4500 1

1995. 174. (wit h Venevitina) , Small motions of an elastic medium in an open immobile container, Zh .

Vychisl. Mat . i Mat. Fiz . 3 5 (1995) , 1095-1107 ; Englis h transl. , Comput . Math . Math . Phys . 35 (1995) , 875-884 . M R 97a:7304 0

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Selected Title s i n Thi s Subserie s (Continued from the front of this publication)

6 A . T . Fomenko , Editor , Topologica l classificatio n o f integrabl e systems , 199 1

5 R . A . Minlos , Editor , Many-particl e Hamiltonians : spectr a an d scattering , 199 1

4 A . A . Suslin , Editor , Algebrai c i<T-theory , 199 1

3 Ya . G . Sinai , Editor , Dynamica l system s an d statistica l mechanics , 199 1

2 A . A . Kirillov , Editor , Topic s i n representatio n theory , 199 1

1 V . I . Arnold , Editor , Theor y o f singularitie s an d it s applications , 199 0