SCIENTIFIC ABSTRACT MURAYEV, E.B. - MURDZHEV, A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001135620013-9
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 13, 2001
• Sequence Number: 13
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

6787~
44~4 / 6 3/020/60/130/06/004/059
AUTHORS: Melentsov,k.A.t and Murayev,E.B.
TITLIz On the Theory of Summation of Double Series by BorelI3 Methods
- \1
PERIODICALs Doklady Akademii nauk SSSR,1960,Vol 130,Nr 6,pp 1193-1195 (USSR)
ABSTRACT:
Lot A be a partial sum of the series
� aik
i-o k-o
to a ik*
Lot the series A(x A converge for all x~>O, y>
ry ik Vk! ,0.
i,kwo
The series (1) is Bp-summable with the sum S if
lim, e A(x,y) - 3, where (x,yk--I-oo means that x-+oo ,
(X 0,Y)k-+00
y-pw in the sector A4Z- (0< A< 1). (1) is called B
r
summable with the sum S if lim e-(X+Y)A(x,y) - S. Let
Card 1/3

67675 4
On the Theory of Summation of Double Series S/02o/6o/!30/06/004/05.9
by Borel's Methods
00 1 k
a(x.y) a x Z- be an entire function. Let VXty)
i,k-o ik !y!
x y
S je-(t+t)a(t,r,)dt dr. The series (1) is Bk-summable with the
0 0
sum 3 if lim Cx9y) . S. If lim 4(x,y) - S, then (1) is
(x$Y)OW X-002ty'"
called BI-summable.
Theorem It Let (1) converge, let it have the sum S and let it
satisfy the conditions
k
ZJI'C*Mi e(1+7%!)y
(4) JfA & 9
k=0 ik k
1-
(5) il%"k
I 4o JL ik i1
where 9 V Nk' h'