# SCIENTIFIC ABSTRACT FOT, A.I. - FETISOV, D.V.

Document Type:

Collection:

Document Number (FOIA) /ESDN (CREST):

CIA-RDP86-00513R000412920015-7

Release Decision:

RIF

Original Classification:

S

Document Page Count:

100

Document Creation Date:

November 2, 2016

Document Release Date:

August 23, 2000

Sequence Number:

15

Case Number:

Publication Date:

December 31, 1967

Content Type:

SCIENTIFIC ABSTRACT

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CIA-RDP86-00513R000412920015-7.pdf | 4.89 MB |

Body:

03
at A. 1.
On.the akebrafe number of cloied extranuds an
A
Mathematical Review a Id Doklady Akad. Ngkuk SSSR (N.S.).,, 89,
" I&
W2_1 I S
.Vol. 14 No. 10 61 1 3). (Russian) , " I ~ I :. , - '. 11 11.
Nov. 1953 Let R be a closed manifold whose t'n v- I first Betti gir mpg
Analysis (mod-2) vanish and whose mth Betti .gioup contains at
least one element of even order. The author's main result
1,o/
is that, given any positive regulai'variational problem for
curves on R, the algebraic nui bar of.closed extremils is
m
not less than 3; and further that there exist'. either con.'
tinuum-many closed extremals of equal length, or else 3
closed extremal~ of indices w -~ 1, 2 (m ~- 1). 3 (m -;, 1),~ This
generalixes, an earlier result In which R was'assumed to be
a 2-sphere [same Doklady (N.S.) 66; 3j7-3SO (1949); these
Rev. 11, 4.7]. The tools needed for this ektinsion Include a
lower es
jimate of dje "length" (mod 2), in the sense of
FroIoffl�nd.E!WI Mat. Sbornlk 42, 63~:192 (1935)11 of
tFe space of!~Iosed non-oriented curyea on R. is "length",
and also the Uwternlk-Schnlmlma~n catEjor~, am' showo
to be not less than 3.' L. a Younj ~( ladisoo, Wi4j,
A. 1.
'A
Author. i : A~ Ij:
Genersuistio~ f; t ~I;im -Theorem on the,
he Undk4hnirellman"
, f
other the-orwa connected with
icovisr n o s -fieres of some
the fomer*
Perlodical
Doki 'AN -S= :95 M9
n 51 21 Apr 1954
Ostract t The the Lusternik-Shnirellman theorem on the
covering of spheres Where-this reflection condition* in'respect~-to
the centerap Is:changiod into an-arbitrary conaition for involute
reflection of,sphares upon themaelves, Some other theorem
related to. this one just mentioned-are also considered.
V. A. .8teklovV I*th. Institute of the Acad, of Scs. of the USSR
fiSubadtted ~5~ fob 1954
T-
Call Nr: AF 1108825
Transactions of the Third All-union Mathematical Congress (Cont. )mo86ow.,
Jun-Jul '56, Trudy '56, v. 1, Seat. Rpts., Izdatel'stvo AN SSSR, Moscow, 1956, 237 PP.
There are 11 references, all of them USSR.
TAkhtenbawn, L. M..(Mosoow), Characteristic Nwnbers of
Improper Graph. :135-136
Smirnov, Yu.,M. (Moscow). On the Extension of
Topological Spaces. 136
Smirnov, Yu. M. (Moscow). On Metrisation of Local
Compact Spaces Which are Decomposable into the Sum of
Countable Number of Sets With Countable Bases. 136-137
Mention is made of Aleksandrov, P. S. and Uryson, P. S.
Eet A. I. (Novosibirsk). Calculus of Variations in the
LFLX;g- e 137
Mention is made of Lyusternik, L. A., Shnirellman, Shvarts.,
A. S., Allber, S. I# and Pontryagin, L. S.
Card 44/80
4L
..-Al4h _;M .M -1
WNR-v M E
.~ a
SUBJECT 'USSR/MATHMTICS/Functional analysis CARD 1/2 PG - 475
AUTHOR FET A.I.
TITLE VnW a-pace of analytic functions and its application to the
Cauchy~Kowalevski problem*
PERIODICAL Uspechi mat.Rauk 11.2 21 215-222 (1956)
reviewed 1/1957
The author shows that the class A of functions being uniformly convergent
in the unit circle, can be changed in a K-space (nee Kaztorovig "functional
analysis") such that a corresponding convergence inside of the unit circle
is identical with the uniform convergence. This permits the application of
general function-theoretioal schemes for the theorem of S.Kowalevski too,
The author proves that the problem
ui I n (k) u N
9t - z r ij + F_ b ij'j + 01
J-1 k-1 -~Xk J-1
Uj(Otxl,-.g,txn) - 0 (1-19 ... IN)
(akj, bijpci are analytic functions of the real variable
i tIx1I---xn in
Itl