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AMERICAN MATHEMATICA L SOCIET Y TRANSLATIONS
Ser ies 2
V o l u m e 8 6
FIFTEEN PAPER S O N REA L AN D COMPLE X FUNCTIONS , SERIES ,
DIFFERENTIAL AN D INTEGRA L EQUATION S
N. I. Ahiezer I. S. Arson Dong Guang-chung
(Tung Kuang-ch'ang) V. F. Gaposkin E. K. Godunova
by
L. D. Kudrjavcev V. I. Levin V. I. Mel'nik S. M. Nikol'skii M. K. Potapov
E. M. Saak G. H. Sindalovskif S. A. Teljakovskif R. M. Trigub G. M. Vaihikko A. G. Vituskin
Published by the
AMERICAN MATHEMATICA L SOCIET Y Providence, Rhode Island
1970
http://dx.doi.org/10.1090/trans2/086
Copyright © 197 0 by the American Mathematical Society
Standard Book Number 821-81786-0
Library of Congress Catalog Number A51-5559
Printed in the United States of America All Rights Reserved
No portion of this book may be reproduced without the written permission of the publisher
TABLE OF CONTENTS Page
Ahiezer, N . I . Extrema l propertie s o f entir e function s o f exponentia l type. [Axwe3ep , H . M . 3KCTpeManbHbi e CBoMcTB a i ejibix <|>yHKu;MM SKCnoHeHl^waJIbHOro TMna. ] Teor . Funkci i Funkcional . Anal , i Pri lozen. 1 (1965), 111-13 5 1
Trigub, R . M . Constructiv e characterization s o f som e functio n clas -s e s . [TpwryS , P . M . KoHCTpyKTMBHbi e xapaKTepwcTWK M aeKO -TOpwx KJiaccO B (|)yHKl MM. ] Izv . Akad. Nau k SSS R Ser . Mat. 29 (1965), 615-63 0 3 1
Arson, I . S . O n the decreas e o f harmoni c function s o f thre e variables . [ApmoH, 1/1 . C. 0 6 ySwBaHH H rapMOHtmecKn x <J>yHKijHf t Tpe x nepeMeHHblx.] Izv . Akad. Nau k SSS R Ser . Mat. 29 (1965), 1 2 8 3-1294 5 1
Sindalovskii, G . H. Differentiabilit y relativ e t o congruen t s e t s . [CwHAaJioBCKWM, P. X . /tM^epeHijifpyeMocT b OTHOGWTejibH o KOHrpySHTHblx MHOatecTB. ] Izv . Akad. Nau k SSS R Ser . Mat. 29 (1965), 11-4 0 6 7
Vituskin, A . G. Representabili t y o f function s b y superpositio n o f functions o f a smalle r numbe r o f var iables . [BMTytUKMH , A. F . 0 B03M0>KH0CT M npeACTaBJieHM H (J)yHKLI,wl l Cynepn03MU,M5IM M (J3yHK ~
UMM OT MeHbQier o MMCJi a nepeMeHHblx. ] Proc . Internat . Congr . Math . (Moscow, 1966 ) "Mir", Moscow , 1968 , pp . 322-32 8 10 1
Teljakovskii , S . A . Som e est imate s fo r trigonometri c ser ie s wit| i quasi-convex coefficients . [TeJlflKOBCKWM , C . A. HeKOTOpbi e OIjeHKM AJI H TpwrOHOMeTpM^eCKW X pflAO B C KBa3MBbinyKJIbIM M
K03(|)(|)MimeHTaMM.] Mat . Sb. 63(105) (1964) , 426-44 4 10 9
Levin, V . I. an d Godunova, E . K . Generalizatio n o f th e Carlso n ine -quality. [JleBMH , B . J/1 , H FoflyHOBa, E . K . 06o6meHn e Hepa -BecTBa KapjicoHa. ] Mat . Sb. 67(109) (1965) , 643-64 6 13 3
Mel nik , V. I . A Tauberian theore m o n larg e indice s fo r th e Bore l method. [MejibHHK , B . M. TaySepoB a TeopeM a o ,,6ojibiuw x noKa3aTejiHx" AJI H MeTOA a BopejiH. ] Mat . Sb . 68(110) (1965) , 17-25 13 7
i n
Page
Potapov, M . K . O n a questio n involvin g equivalenc e o f condition s for convergenc e o f Fourie r se r i e s . [llOTanOB , M . K . K BOnpOC y 0 6 9KBMBaJieHTH0CT M yCJIOBW M CXOAMMOCT M pHAO B $ y p b e . ] Mat .
Sb. 68(110 ) (1965) , 111-12 7 14 7
Gaposkin, V . F . O n serie s relativ e t o th e system \(£>(nx)\.
[ranoojKMH, B . $ . 0 pnaa x n o cwcTeM e \cf>(nx)\.] Mat . Sb . 68(110) (1965) , 328-35 3 16 7
Kudrjavcev, L . D . an d Niko l ski i , S . M . Imbeddin g theorem s an d their applicatio n t o solvin g ellipti c equations . [KyApflBljeB , JI. fl. M HttKOJIbCKHM , C . M . TeOpeMb I BJIO>KeHW H M MX npMJIO -
>KeHwe K peiueHWK ) ajuiwnTuqecKwx ypaBHeHMM. ] Izdat . Sibirsk . Otdel. Akad . Nau k SSSR , Novosibirsk , 1961 , pp. 87-10 9 19 9
Saak, E . M . O n th e regula r approximatio n o f solution s o f comple x elliptic equation s o f arbitrar y order . [CaaK , 3 . M . 0 peryJIHp -HOM annpoKCMMai w w peiueHW M KOMnJieKCHbi x sjuiwnTimecKM X ypaBHeHMM JiioSor o nopHAKa. ] Ukrai n Mat . Z . 1 8 (1966) , no . 6 , 26 -40 22 9
Vaniikko, G . M . O n th e rat e o f convergenc e o f certai n approximatio n methods o f Galerki n typ e i n a n eigenvalu e problem . [BailHMKKO , r . M . 0 6bICTpOT e CXOAMMOCT M HeKOTOpbl X npn6jM)KeHHbI X
MeTOAOB Tun a FajiepKWH a B npoGjieM e co6cTBeHHbi x 3HaqeHMM. ] Izv. Vyss . Ucebn . Zaved . Matematik a 1966 , no . 2 (51) , 37 -4 5 24 9
Dong Guang-chan g (Tun g Kuang-ch'ang) . Uniquenes s theore m fo r th e
Caplygin problem . I [ f * i : 3 E At f t &7? t& ft t — *fe Jg M
(I).] Act a Math . Sinic a 6 (1956) , no . 2 , 242-24 7 26 1
Dong Guang-chan g (Tun g Kuang-c h ang) . Uniquenes s theore m fo r th e
Caplygin problem . I I [ | t % 1 : It * * £ ~fS tlk f# * £ — « • 5 E i §
(II).] Act a Math . Sinic a 6 (1956) , no . 2 , 250-26 1 26 9
IV