SCIENTIFIC ABSTRACT VLADIMIROV, V.S. - VLADIMIROV, V.YA.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001860220002-0
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 14, 2001
• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

29897
SA1 61/060/000/0-03/009
2 B112YI3125
AUTHOR: Vladimirov, V. S.
TITLE: Analytic completion for special domains, its coristruction
and application
SOURCE: Akademiya nauk SSSR. Matematicheskiy institut. Trudy.
v. 60, 1961, 101 - 144
TEXT: Various proofs of dispersion relations, introduced by Bogolyubov
into quantum theory in 1956, are based on the construction of an analytic
completion of a given domain G. In the present paper, the author carries
out such a cinstruction for domains of a special kind. A domain G is said
to be analytic if there is a function that is analytic in G but not in a
domain including G. The analytic completion H(G) is the greatest domain
including G, which is contained in the intersecti-on of the analytic domains
of all functions that are analytic in G. The convex completion K(G),
which belongs to a given class K of functions, is the greatest domain in-
cluding G, which is contained in the intersection of the analytic domains
of the functions of K that are analytic in G. The author considers domains
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2~oj 07
S/51 61/060/000/003/00,q
Analytic completion for &pecial B112YB125
i - +
having the form TkjG. T and G are defined as followst T - T -.-j,T
T� = Rn+1 + i where Rn+1 is the (n+l)-dimensional real Euclidean space
with x = (x0 x I...,x n) as its points is the set of all points x, for
which x2 > 0 and x0t 0 are valid; Gc R n+1 ; U is a certain domain con-
taining G. The author constructs the completion K(TQ G-) wi,th the aid of
the corresponding integral representation
f ip (p', ).) 2L p')2 ell;'dX + P (7.15
0
.0"
0
+ n+L,' + (p', X) dp~dl,
2'~
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. . . . . . . . . . . . . . . . . . .
877
3/517/691 060100010031009
Analytic completion for special ... B112/B125
L is the operator that is inverse to the operator _i- ; PT is an
0 afo
arbitrary polynomial whose degree depends on the function f; t are weight
functions. Finally, the author applies his results to differential
equations. I. M. Gellfand, G. Ye. Shilov (Obobshchennyye funktsii, vyp. 1
i 2. Fizmatgiz 1956), N. N. Bogoly-ubov, D. V. Shirkov (Vvedeniye v teoriyu
kvantovykh poley, GTTI, 1957), and S. L. Sobolev (M6thode nouvelle A
r6soudre le probl4me de Cauchy, Matem. sb., 1936, I(Ai)l 1, 39 - 72) are
referred to. N. N. Bogolyubov and 1. T. Todorov are thanked for assist-
ance. There are 38 referencest 13 Soviet and 25 non-Soviet. The three
most recent references to English-language publications read as followil
H. J. Breinermann, R. Oehme, J. G. Taylor. A proof of dispersion relations
in quantized field theories, Phys. Rev., 1955, 109, 2176 - 2190; F.J. Dyson.
Integral representations of causal commutators. Phys. Rev., 1956, 110,
1460 - 1464; R. F. Streator, Special methods of analytic completion in
field theory. Proc. Ray. Soc., ser. A, 1960, !!L~, 39 - 52.
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VLADINIPDV, V.S.; NIKITIN, V.F.
Jost-Lehmann-Dyson's integral repreBentation. Dokl.AN SSSR 138
no.&iIS09-812 Te 161. OaFA 14:5)
1. Matematicheakiy iuBtitut imeni V.AjSteklova AN SSSR. Predstavleno
akademikom N.N.Bogolyubovyme
(Topology)

VLADIMIROV, Vasi.liy Sergeyevic'; TODOROV, I.T., red.
(Methods in the thcicni of functione cf nevcrLl com:,Iex
variables] Metody teorii funktsli umogikh korplekerjykh
peremevinykh. Moskva, Nauk-a, 1964. 411 p.
(IAIRA 17:10)

SAMUNDZHANy Ye.M. (Eyevj ul. Ordzhonlkidze, d.3, kv.53);
VLAD V.S. (Eyev, ul. Or-dzhonAJidze, d.3,, kv.5)
___)~qROVA9
Functional state of the adrenal cortex in benign and malig-
nant tumors of: the uterus and ovarips. Vop. onk. 10 no-3%93~-98
164. (MIRA 17:8)
1. iz Ukrainskogo nauchnc~--issledovatellskogo instituta
skoperimentallnoy -! klinicheskoy onkologli (dir. - akademik
AN UkrSSR prof. R.Ye. Kavetokly! f. K~_'y(,v.9kcgo ran f'gerioradiolo-
gicheskogo '" onkolog-Ichesk3go "nsti.tuta (dLr. .- prof, 1.T.
Shevchenko).

VLADIMIROV, V.S.
Corrections to V.S. VI-adim:Lrovis article nFunctions, holo-
taorphic in tubular cones.tl Tzv, AN SSSR. Ser. mat. 27 no.5%
1186 -0-0 163. (MIRA 16:11)

VLADIPU94-Y.,$. (Moskva); SHIRIMMOV, M. (1403kva)
Construction of holomorphy envelopes for Hartogs regions* Wwo
mat. zhur. 15 no.2:189-192 163o ~ (RIRA 160)

VLADIMIRGV.-YA,,,, insh; KCSOY, Yu."... insh.
Choice of voltage and power rating for pole pairs of plaatiog
current motors. Vest. edektroprom 34 no.6:20-21+ Je 163.
(MIR& 16:7)
(Electric railway motors)

VIADIMIROV V,S,
Functionss holomorphic in tubular cones. Izv.AN SSSR.Ser.mit.
27 no.lt75-100 Ja-F 16). (MMA 1622)
(Functions, Analy-tic) (Cone)

. VLADIMIROV2 V.S.
On Bogoliubov's "edge of the wedge" theorem. Izv.AN SSR.Ser.mat,
26 no.6a825-838 N-D 162. (MIRA 15S12)
(Quantum field theory)

ALEKSANDROV, P.S., red.; BOLISHEV, L.N., red.; VLADIMIIIQV,-Y.S..-red,_L-
KUD.RYAVTSEV, L.D., red.; LEONT'YEV, A-.F-.,red.; IIIKOLI~KIY, S.11.1
rod.; POSTNIKOV, M.M., red.; SOILVENTSEN, Ye.D., red.; SHAFAREVICH,
I.R., red.; GRIBOVA, M.P., tokhn. red.
(English-Russian Eathematical dictionary]Anglo-russkii slovarl ma-
tematicheskikh terminov. Red. kollegiia; P.S.Alaksandrov (predse-
datell) i c1;. Moskva, Izd-yo inostr. lit-ry, 1962. 369 p.
(MIRA 15:11)
1. Akademiya nauk- SSSR. Matematicheski-y institut.
(Engliab language-Dictionaries-T-lussian)
(Mathematics-Dictionaries)

VLADINMO-V, I.S.-
Some variational methods of an approximate solution of the
transport equation. Vych.mat. no.7:95-114 161. (,IURA, 15%4)
(Distribution (Probability theory)) (Calculus of variations)
(Approximate computation)

VLADIMIROV., V. A.
"Some generalizations of the Paley-Wiener-Schwartz theorem"
report submitted at the Intl Conf of Mathematics, Stockholm, Sweden,
15-22 Aug 62

AUTHOR: Vladimirov, V. S.
3/04 62/Ooo/oo6/o47/127
'Pi 56Y31 12
TITLE: Mathematical problems of single-velocity theory for the
tranofer of particles
?--'RIODICAL: Referativnyy zhurnal. Matematika, no. 6, 19062, 95, abotract;
6B403 (Tr. Iylatem. in-ta. ;~N SS9R, v. 61, 1961)
TEXT; This is a monograph in which a mathematical theory is produced for
one class of boundary problems for inte6ro-differential equations with
first order partial derivatives. This class of problems depic.ts various
physical processes, among which in particular are them transfer of
neutrons in subs-'lances, the scatterinn- of light in the atmoGplierQ, the
radiation
in
j_ssaz~3 of 1~_rays throuOh diffusing media, the transfer of
stellar atmosphere, and cosmic ray showers. '.7hen interpreting the.
mathematical results, 'he process of transfer of neutrons is borne
2rincipally in mind in the problem of calculating for nuclear reactors.
It is assumed that: (1) the bounded re,3ion G in which the process of
transfer of neutrons takes place is convex and bounded by 'he piecewise
smooth surface B; (2) the velocities of the neutrons are identical;
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3/0 4 4 /62 /1, 000/04 7 /12 7
:;,athematical problems of sin`~Ic- B156/BI 12
~'
the indicatrix of" scattering depends or, the directions -V V S,
and -S"' = 411 vli -1 of the velocities `V` anti 11 only throuah the cosine of
the an-le between them, Ii = (S's'); (4) no external flow of neutrons
0
impingaz on B. On these azsumptions, the integro-differenlial equation
(s,grad~) +,f 0(P,p')f(o,P)ds' + F(s,?)
4r, 0
is obtained; in this ectuation the boundary conditions are I((s'2) = 0'
-n ) < 0 ( A i - 1,
-~ I -(3, the unit vector of the external nornal), where the
unknown function u(s,-;') denotes the density of the particlez leavin- the
i,oint P = (xj 'x 21X3 G in the direction -9% 61u(t,, is the unit sphere with
its center at the ori'--r of the coordinates of three -d imens ional Euclidean
Svace); the function a(.?), whici si-nifies the absorption of the medium,
.U
is Lzeasurable, positive, and bounded almost everywhere on T,; the kernel
U3(P,go), which characterizes the anisotropy of scatterin,'-q is a def,'enerate.
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z4athematical problems of single-...
3/04 62/000/006/047/127
B1 56yi3112
n
kernel
O(P' 40) bi(P)Oi(PO),
0i(g0) is int~gpable on [-i,+'] and b,(P) is measurable and bounded
almost-everywhere on G; the function F(S,P), which signifies th6 intensities
of thd"nources, is integrable with the power p(1,