SCIENTIFIC ABSTRACT KAZMIN, YU.A. - KAZMIROWSKI, A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000721410012-3
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 13, 2000
• Sequence Number: 12
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

8619f
,1
S/055/6o/coo/005/001/010
Cill/C222
16,1000 ~b
XUT11OR: Kaz'm1nj Yu-A~ f AnalytiS~ Functions. I
On the Completeness of a SY ~eul 1~ r ul-
TITLE: teta- Seriya It mat-ematika,
pERIODICAL: Vestnik ~Joskovskogo universi
mekhanika, 1960, No-59 PP-3-15 6ion A by translation
te the region arising from the re V. (A+ oc. r- D)
TEM. Let A+o4deno Let A+Vlc-D. Let a certain set of points
with the vector Of,,. one point and let V - 0(-K(A)'
form a Continuum K(A) not degenerating in stems of functions Jrf
(Z+CG)j
1: Let f(,z) be regular in D, The sy L n
Theorem rent points
~f(n)(z) e is an infinite bounded set of diffe
and .1 wher (Y'n T ot in A CD-
/-K(k), are simultaneously complete or n
Theorem 2: If f(z) is regular in D and
(1) tf (.z)l9 on A+OCCD-
is complete in Ar-D, then (1) is complete in an arbitrary regi
~f(n)(Z)~ and {f(n)(Z-0')1' n.0,1,2,.,, are
Theorem 3t The systems t in kC-D if f'~- n n and
simultaneously complete or no njC K('),
Card i/4
86
3/055/60/00V005/001/010
C111/C222
On the Completeness of a System Cf Analytic Functions. I
co
A X Co ; or I ~'
n n+'V co, but there exists a circle
n.0 n-o
0(' - r, r >O, lying in K(A), so that
U-m n ~L r
n -? OD e
Let f(z) be regular in D and representable as the limit value of
a
sequence, converging uniformly in D, of Dirichlet polynomials
P ?Vi z
(8) Pn(z) anje
J.1
with given A J-1,2,-- Let in D to every .3equence rn (z)
converging
uniformly to f(z), correspond uniquely the series ~_-a j eA'jz,
where
a. - lim a e., in D there exists a sequence of 1--near
fun-.tionals L
J n --~co nj' n
Card 2/4

86195
3/055/60/000/005/001/010
C111/C222
On the Completeness of a System of Analytic Functions.. I
so that L [e ,e . Lst
n C'nj
'J'] i
L r. -
nL
L
where L is a rectifiable curve it D and (Z)
iy'n AI(L) ; M(L) is the set of
funr,tions defined on L for which a certain additional
condition ia
satisfied (to M(L) there belong e.g. functions being of
bounded variation
on L).
Theorem 4, For a 0, the closed linear closure of the system
ff(")(Z)~
oontains the closed linear closure of the sequence Je in every
region A,
where K(A)-)L,,
Theorem 5x Let f(z) in 3 1 --oc>