SCIENTIFIC ABSTRACT KOSTYUCHENKO, A.G. - KOSTYUCHENOK, B.M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000825310013-8
• Release Decision: RIFPUB
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: January 4, 2017
• Sequence Number: 13
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

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~,;ultidimensional Problem of ~:oments

8oo74
$/020/~0/131/'0~/00~/071

where ~- is a uniquely defined measure on the k-dimensional torus Sk.
Definition: The sequence s , n = O, 1, .... (Sn~O) is called
seouence of the ~uP K, ifn

(4)
. � "' ~ ~o

Theorem 7: Let T , n = (nl,...,nk) be a k-fold sequence for which
a.) ~' -,.. ~ .. ' 0.. :'.'h~rc.~ ~,~, n = O, 1, ..., N i~ r.n ~:~..bitrary
" ' for ever5 m the sequence

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C~A-RDP86-005~3R0008253~00~3-8

8o07~
S/020/~0/1~1/0~/00~/071
~ultidimensional Problem of ~oments

with the index n~, j = 1, ..., k, is a sequence of the type K. Then
it holds the z. ep~esent~tion

where the measure ~- is uniquely defined.
A. ~.;. ~(olmogorov, Ye. Vul and Gel'land are mentioned in the paper.
There are 10 references: 7 Soviet and 5 American.

.kSh. OCIATION: ~,~oskovskiy gosudars tvennyy universi tet imeni t.[.V.Lo::~onosova

i~RESE~?rED: December 20, 1959, by S. L. Sobolev, Academician

SUBJ.iITTED: December 25, 1959

Card

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,, 800~0
/(,. %.~ 0 0 o/0 20/60/1 ~ 2/01/0 7/0 64
AUTHOR: Kost~uchenko, A.G.

TITLE: Ev&luation of the Resolvents of Singular Elliptic Operators
PERIODICAL: Doklady Akademii nauk SSSR,1960, Vol. 1S2, No. 1, pp. 32-~5

TEXT: Let
: ~ "kn(x)
0
'' kl+~.o+kn=2m 9Xlkl'''~x~nn

kl...kn
where x = (Xl,~.~,Xn) , - ~O I Ix.-yJ~l ; c~O t B~ - constant. In the neighborhood of
x=y, H(x,y) has the singularity of the fundamental solution. Theorem 2 s
kl.ook
Let the matrices A n(x) be symmetrical~ let a) and b) be satisfied ;

2m-1

2m

n(x) 91
m1 mn
~x1 ... xn
B1 , for ~>0 let be valid

(x) , 1 = 0,1,..., 2m - 1 .

let Q(x) satisfy (1). Let
for th~ elements bij (x)

(4) I~. (x)lg o g
zj~l
Cara 3/4

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aoo o

Evaluation of the Resolvents of Singular
Elliptic Operators

, 2m-1
Th;n the opera~or ~ = L + ~ Bi(x, ~) has a complete eystem of o

eigenfunctions, and adjoined functions.
The author mentione M.V. Keldysh.
There are 5 Soviet references.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet imeni M.V. Lomonosova
(Moscow State University imeni M.V. Lomonosov)
PRESENTED: December 28, 1959, by S.L. Sobolev, Academician

SUBMITTED: December 25, 1959 ~

Card 4/4

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16,

AUTHORS

Kostyuchenko: A,G,,,. and Eskin, G ~

TITLE:

Cauchy's problem for Soboiev..Ga! per:', equat, lon~

SOURCE:

r,Ioskovskoye matema;ichcskoye oOsn