SCIENTIFIC ABSTRACT BERNSHTEYN, S. N. - BERNSHTEYN, V. M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000205020010-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 8, 2000
• Sequence Number: 10
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

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PM/Nathellition SWI08 Nov 1947
Mthematics Formalas
~Mmiting Laws for Meox7 of Optimum,
ApproxImations,"
an S. N. BOMB
pg. 4ademici hteyn, 4 pp
:"~Dok Ak Naue voi Lvni, wo 4
thor has previous3,v stated that,the
11mitirig law I
fft) ~=A T. f CZ) can be applied to the.
P*C F
'~Vunetlonf 6E)(-
If for all'values of r>o
is a limited equa4ity. This is a continuation
an artiole published 1n *Dok Ak NWAI Vol
IaVj, No
1946, In which he showed that the first
fopmaa
-~q= be used for all cases vhere the
function x
I/Mathematics Series ..(Cmtd) Nor 1947
'Ills the requiremmt /ffX)k9&)(- c;04 X 4 0-
vhere HW Is a whole funo-
L of a zero series. Submitted 9 Nor 1947.

StrengthenivC the theorem on surfeces of a
negative curvature.
Veh. sap. IOU nv.96.-75-81 048. (MLRA 10!8)
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6F-RNS1i-rEYJ4,,.'S -N
PHASE I TREASURE ISLAND BIBLIOGRAPHICAL REPORT
BOOK Call No.:
Author: BERNSHTEYN M-
Full Tit LLECTED-WORKSp VOL. I. CMSTRUCTNI
(1905-1930)
Transliterated Title: Sobraniye soehineniy. Tom I.
teoriya funktsiY (1905-1930)
AID 547 - I
QA3.B5
THEORY OF FUNCTIONS
Konstruktivnaya
PUBLISHING DATA
Originating Agency: Academy of Sciences, U.S.S R.
ftblishing House: AcadenW of Sciences,, U.S.S.R:
Date-z 1952 No. PP.: 581 No. of copies: 3,000
Editorial'Staff: Prof. N. I. Akhiyezer, Prof. V. L. Goncharov,
Prof. A. N. Kolmogorov, Prof, S. M. Nikollskiy and Prof. I. G.
Petrovskiy; also Kand. of Physic.-Nath. Sci. V. S. Videnskiy
PURPOSE: Not mentioned
TEXT DATA
Coverage: The volume contains 49 papers and articles (1905-1930)
covering the constructive theory of functions and together with
the second volume (62 items) (AID 495 - A fully.presents
Bernahteyn's investigations in this field. The book contains
also a large number of the author's remarks and explanations
pertaining to his articles In the text (38 pages), and an
1/2

Sobraniye soohineniy. Tom I. Konstruktivnaya AID 547
teoriya funktaly (1905-1930)
enumerated list of 265 of his works in chronological order from
1903 to 1952 on various subjects (12 pages), in Russian and non-
Russian languages, with indication of the periodicals of publi-
cation. The 49 articles were previously published In a number
of periodicals, mainly non-Russian.
No. of References: Very numerous in footnotes In the text.
Facilities: None
2/2

I
-2-22-2- ~--

BMISHTEYN, S. N.
PA 233T91
USSR/Mathematics -An'timajorants Nov/Dec 52
"Antimajorants," Acad S. N. Bernshteyn
."Iz Ak Nauk SSSR, Ser Matemat" Vol 16, No 6, pp 497-
502
-The article contains a demonstration and generalizathn
.of one theorem on antimajorants which was formulated
earlier by the author (cf. "Majorants of Finite or
Quasi-Finite Growth," "Dok Akad Nauk SSW Vol 65,
1949, pp 117-120). The name antimajorant (H(x) in
set A) is given to each function H(x)>,O(-ootxcoo)
possessing the property that the inequality of the
form /~(-NJH(x) for all x, where sup/G'/>N on any
inter a 2a, P
233T91

Bank& S. N. . On normikilly Inaeasing weight funtdons
WW Offinite, gmw&., DoWady AW. Nak
SSSR (N.S.) 35 257-260 (1952). (Russian)
The author c;;elates a number of his recent results on
weighted polynomial approximation and on inequalities
for
entire, functions [same Doklady.'(N.S.) 6S, 117-120; 66,
545-5.49 (1949); 17,549-552, 773-776 (1951); these Rev.
11,
23; 12, 814; 13~ 26] "'d-one of Videnskil's [see the
preceding
review3. In even functions t(x) of N [normal
increase: see the third. reference cited above] are
either in
class Nj,'majoiizing on the real axis some ev Ien entire
FI(s)
with positive coeffi6ents in its power series and not of
genus
zero; or in class N~ majorized on the real axis by Fo(s)
of
the same kind as PI(s) but of genus zero. The author
then
considers the'clasi N* of functions-4Kx) of N which
belong
to No forx>o andto N, for x