AMERICAN MATHEMATICA L SOCIET Y TRANSLATIONS

Series 2

Volume 9 3

N I N E PAPER S O N FUNCTIONA L ANALYSI S

by

Ju. M. Berezanskii A . G. Kostjucenko D . A. Raikov M. M. Dragilev M . G. Krein V . Ja. Stecenko A. R. Esajan B . S. Mitjagin B . E. Veic

Published by the

AMERICAN MATHEMATICA L SOCIET Y Providence, Rhode Island

1970

http://dx.doi.org/10.1090/trans2/093

Copyright © 197 0 by th e American Mathematica l

Library o f Congress Catalog Numbe r A51-555 9 International Standar d Boo k Numbe r 0-8218-1793- 0

Printed i n the United State s of Americ a

All Rights Reserved

No portion of this book may be reproduced without the written permission of the publisher

TABLE O F CONTENT S

Page

Kostjucenko, A . G . an d Mitjagin , B . S . Positive-definit e functional s

on nuclea r spaces . [KoCTfOqeHKO , A . T . M MwTHrHH, B . C .

noJio>KWTejibHO-onpeAejieHHbie (JjyHKuwoHajib i H a H/jepHbi x npo -

CTpaHCTBax.] Trud y Moskov . Mat . Obsc . 9 (I960) , 283-31 6 1

Mitjagin, B . S . Nuclearit y an d othe r propertie s o f space s o f typ e S .

[MwTarwH, B , C . HAepHocT b w flpyrwe CBoftcTB a npodpaHCT B

Tuna S. ] Trud y Moskov . Mat . Obsc . 9 (I960) , 317-32 8 4 5

Dragilev, M . M . O n regula r base s i n nuclea r spaces . [/JparmieB ,

M. M . 0 npaBWjibHbi x 6a3wca x B HAepHbi x npocTpaHCTBax. ]

Mat. Sb . 68(110 ) (1965) , 153-17 3 6 1

Veic, B . E . Besse l an d Hilber t system s i n Banac h space s an d ques -

tions o f stability . [Beta; , B . E . CwdeMb i Becceji n w Tmib -

6epTa B npocTpaHCTBa x BaHax a w Bonpoc w ycTOMqwBOCTM. ]

Izv. Vyss . Ucebn . Zaved . Matematik a 1965 , no . 2 (45) , 7 -2 3 8 3

Krein, M . G . Introductio n t o th e geometr y o f indefinit e / - space s

and t o th e theor y o f operator s i n thos e spaces . [KpeMH , M . T .

BBeAeHne B reoMeTpwi o wHAecjMHWTHbi x 7-npocTpaHCT B w TeopwK)

onepaTopOB B STM X npocTpaHCTBax. ] Secon d Math . Summe r

School, Par t I , Naukov a Dumka , Kiev , 1965 , pp . 15-9 2 10 3

Krein, M . G . O n som e ne w Banac h algebra s an d Wiener-Le'v y typ e

theorems fo r Fourie r serie s an d integrals . [KpeilH , M . T . 0

HeKOTopbix HOBW X BaHaxoBbi x ajireSpa x w TeopeMax Twn a Teo -

peM BwHepa-JIeB M jyin PHAO B w wHTerpajio B $ypbe. ] Mat . Issled .

1 (1966) , no . 1 , 82-10 9 17 7

Raikov, D . A . Exponentia l la w fo r space s o f continuou s linea r map -

pings. [PawKOB , J\. A . BKcnoHeHUiMajibHbi M 3aK0 H AJI H npocT -

paHCTB HenpepbiBHbi x jiwHeMHbi x OTo6pa>KeHHM. ] Mat . Sb . 67(109 )

(1965), 279-30 2 20 1

i n

Berezanskii , Ju . M . O n a n eigenfunctio n expansio n fo r selfadjoin t

operators. [Bepe3aHCKHM , K) . M. 0 pa3jio)KeHw w n o co6cTBeH -HHM $yHKijj/iH M caMoconpa}KeHHbi x onepaTopoB. ] Ukrain . Mat . Z. 11 (1959) , 16-2 4 22 7

Stecenko, V . Ja . an d Esajan , A . R . Theorem s o n positiv e solution s

of equation s o f th e secon d kin d wit h nonlinea r operators .

[CTeqeHKo, B . H. w Ecajw, A . P. TeopeMb i o nojio>KWTejib -HHX peiueHwa x ypaBHeHw w BTopor o poA a c HejMHeftHbiM w onepa -TopaMH.] Mat . Sb . 68(110 ) (1965) , 473-48 6 23 9

IV