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

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001860220001-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 14, 2001
• Sequence Number: 1
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

b0(',Ll:!IAVSKIY,f B.I.; 'i-1, i'~."N.p 'inzli.,, retnenzarit;
VLADINIROV, V.M.p inzh.0 red.
(Automatic rmichines an, o,~r-rall a-utoration] A-1tomaty I
komplekonaJ avtovatintoiia. ll'oslntn, Ezohinostruenio,
1964. 534 P. (Ilial, ].,/:ii)

ANUFRIYEV, V.A.; KHITRWI, N~M,; 01,1KHOVISKIY, N.V.; BOLUTIN, A,I_
inzb... retsenzent; VLADIM11-1,0V V.14.;, InzYj., red.
(Large-lot production of milling machines] Krupnoserilnoe
proizvodstvo frezernykh stankov. Moskva, Mashinostroenie,
1965. 206 p. (MIRA 18:4),

RABKINq A.L.; FEDOTENOK, A.A., prof.t retsenzentj )WIMIM's-VOM.0)
inzb., red.
(Relieving machine tools] Zatylovochnye otanki. Voskva(
Mashinostroenie, 1964. 148 p. (MIRA 17tl2i

VLADMIROV, V. M.
Vladimirov, V. M, - OThe scientific-methodological conference in the Moscow Power
rnatitute"p (January 1949). Vestalk sysah. shkoly, 1949v No. 4y p. 43-46.
SO: U-4113, 17 -Tuly 53, (Letopis 'Zharnal Inykh Statey, No. 20, 1949).

VIADIMIROV. V.)(.; GULYAYAV, Y.I.; ROGANOV, G.N.. radaktor
%"t ~ a P &~M~- Im -
- 'mWAW
[Appliances and mechaniaze adapted to the work of invalids]
Prispopobleniia i mekhanizaW. oblegehayushchis trod invalidov.
Pod red. G.N.Roganove. Moskva, [Xoix] 1955. 155 P. (MIRA 10:3)
(DIUBI&D--MMABILITAT ION, ITO.)

DASHCHENKO, A.I., kand. tekhn.nauk~_VLA!j V, VM,,-.-inzh., ved.
red.; APIRIN, B.S., inzh., red.; PONOMARZV, V.A., tekhn.red.
(Power heads for small semiautomatic machine-tool units]Silovye
golovki malykh agregatnykh poluavtomatov. Moskva, Filial Vses.
in-ta nauchn. i tekhn. informataii, 1958. 75 P. (Peredovoi na-
uchno-tekhnicheskii i proizvodstvenn;~ opyt. Tema 10. NO-M-58-59/11)
(miRA 16:2)
(Machine tools)

VL&DIMIROV. V.M.
~-",.
flew technological processes And autbmAtic equipment for finish-
ing wooden articles. Biul.tek~i.-ekon.inform.Gos.nauch.-iLsl.
inst.nauch. i tekh.infom. 16 no.10:59-65 163. (MIRA 16:11)

VIADIMIROV,, V,B., inzh.
Automatic control of a hydraulic press. Av-t. dor. 26 no-5:25
My 163 e (IffRA 16:7)
(Hydraulic Presses) (Automatic control)

IRMON, V.D.; POLYVYANNYY, I.R. - YIADIMIROV, V.P.
-
- -
Effect of the rate of air auction on t~e-"p-r~-o`ce'-ss data obtained in
sintering lead sulfide concentrates. Iry.AIF Kazakh.SM Ser.gor.
dala. met.stroi.i strimat.no.9:53-61 '56. (KMA 10:2)
(Lead--Ketallurg7) (Sintering)

IV,OL 0 1,,Afd /X /', ii j~_ /-7
'j- -- -'-
BUDON. V.D.; POLYVYANNYT, I.R.;.,VLA.DIMIROY. V.P., .
~ "-., - -
Zffect of charge column height on the process data ottaned in lead
sulfide concentrates. Izv.AN Irazakh.S= Ser.gor.dela, met.strol.1
stroinat.no.9:62-69 '56. (HLRk 10:2)
(Lead-Metallurgy) (Sintering)

Vl;,',.DT!'T':CjV, V-P-; C nd T(.-cli rici 4d i 7, r t -J r,. tlwi:;wa dn ta on
19-50. 20 -.,'-'th
Ilon-
Ucad of Sci Kap SR. Im-,titute of lnt~,llur,-y dd Cbncon
tr.,Ition), 150 cu_,Joo (:'].,29-51), 12-5)
-33 -

18(5)
AUTHORS: Vladimirov, V.P. and Ponomarev, V.D.
TITLE: Heat Content and Smelting Temperatures of Slags of the
SiO -FeO-CaO System (TeDlosoderzhaniye i temperatury
N
e
leniya shlakov sist
my SiO 2-FeO-CaO)
pl
PERIODICAL*: Vestnik Akademii nauk Kazakhskoy SSR, 1959, Nr 2,
pp 100 - 106 (USSR)
ABSTRACT: This is a report on an experiment carried out to
establish the smelting conditions and the heat content
of slags of the triple system SiO -FeO-CaO. The
&
slags of non-ferrous metallurgy
mostly lime and
iron containing silicates. Generally, the total
cutput of the system SiO 2-FeO-CaO represents 80 -
90% of the weight of the materials to be smelted.
It is obvious, therefore, that the qualities of this
system determine to a considerable degree the slag
qualities of non-ferrous metallurgy. In order to
prepare slags of the system SiO 2-FeO-CaO, the authors
Card 1/4 used the followinC materials: a synthetically pre-

'30V/31-59-2-12/17
Heat Content and Smelting Temperatures of 'Slags of the SiO 2-Feo-Cao
System
pared silicate containing 66. 8~10 FeO, 6,-~ Fe 0 1
Fe ~e~ and 26.160,o' SiO 2, a purified rock cryMl'
(9 - 55/a SiO ) and chemically pure calcium oxide.
These mater?als mixed at an established ratio were
molteR in a Tammann furnace at a temperature of
1,300 OC. Roasting of the slags at a temperature
of 950 permitted elimination of the cooling require-
ments, made on the degree of crystallization of the
materials. It was Dossible to avoid thereby dropping
the heat content magnitudes. The special riethod
used in this case made it pQssible to characterize
the process under its quantitative and qualitative
aspects. The heat content of the slaCs was getermined
within a temperature interval of 200 - 1,250 . The
roasting of the slags and the experiments were carried
out in an argon atmosphere. Altogether, 40 synthetic
slags were examined. The results of the investigation
were the following: 1) The output of Si eO-CaO
t.) ~2_-F
slags smelted at temperatures up to 1250 C varies
within the limits: SiO 30-60'.0, FeO 15-60%, CaO
Card 2/4 8-30'/,); 2) the heat co~_tent of the slags below the

S-OV/31 -59-2-11 2-0/117
Heat Content and Smelting Temperatures of Slags of the SiO eO-CaO
System 2-
temperature of their first melting phase obeys the
law of additivity; 3) the heat content of the molten
slags changes at a temperature of 1,2500 C from
340 to 400 cal/g, depending on their chemical com-
position; calcium oxide has the greatest influence
on increased heat content; 4) the initial and final
temperatures of the smelting process have been estab-
lished; isotherms connecting the full melting points
of the slac-, components have been plotted on a tri-
ang 0
,ular graph; 5) the possibility of using the
heat current method for a simultaneous determinat4 on
of the heat content, the initial and final smelting
temperatures and also the melting heat of the sub-
stances, shows its advantaCe over other methods;
6) the obtained graphs (heat content an& viscosity)
permit singling out a section of the trian~rle, where
the slags have a comBaratively low melting temper-
ature (1,000 - 1 ,150 ) and a respectively low heat
Card 3/4 content (340-3,"0 cal/g); the output of these slags

1 - 519-2-12/17
Heat Content and Smelting Temperatures of Slags of the SiO 2-FeO-CaO
System
varies within the following limits: SiO - 35-53%,
FeO - 30-55%, CaO - 7-25~5; 7) the resuits obtained
with regard to the fusib=ty and heat content of
slags of the triple system permit selection of the
most suitable slag composition under Droduction con-
ditions. In the article the following scientists
are mentioned: Kh.K. Avetisyan, Professor I.M. Ra-
falovich, B.P. Selivanov. There are 6 graphs and
5 Soviet references.
Card 4/4

SHIJRGVSKIY., V.G.; VIPIMOV., VJ~*; GNATYSHERKO., G.I.; MOCHKIN., A,F.;
SHCHUROVSKIY, Yu#Ae; ADSON., H.1,; GOLOVKO; V,V.
Sow physicochemical properties of charges for and the productr of
the electric smelting of Dzbezkazgan copper concentrates. Izv4.AN
Ka--"akheSSR.Ser.,met,,,, obog.i ogneup. no.ls&-.13 161. (KMA 14 86)
(Dzhezkasgan--Copper-Electrometa.Uurgy)

2V
POLTVYAIIIIYY, I.R.; VLADIMIROV, V.P.
Studying the rate of oxidation of lead sulfide concentrates. ISY.AN
Kazalth.SSR-Ser.gor.dela met., stroi. i stroimat. no.4:109-124
157. (Lead sulfide-,Hetallurgy) (Oxidntion) (MM 11-4)

SOV/ 137-58-7- 14079
Translation from: Referativnyy zhurnal, Metallurgiya, 1958, Nr 7, p 14 (USSR)
AUTHORS: Polyvyannyy, I. R. , Vladimirov, V. P.
TITLE: A Study of the Rate-o-'MMidation of Lead Sulfide Concentrates
(I:~ucheniye skorosti okisleniya sul"fidnykh svintsovykh kontsen-
tratov)
PERIODICAL: Izv. AN KazSSR. Ser. gorn. dela, :rnetal lurgii, str-va i
stroymaterialov, 1957, Nr 4 (15); pp 109,-124~
ABSTRACT: The object of the investigation is to study the overall oxida-
tion rate (OR) of Pb-sulfide concentrates, and also the OR of
individual sulfides in these concentrates in accordance with the
temperature, duration, and chemical and mineralogical composi-
tion of the concentrates. When the concentrates are roasted
under conditions of gradually rising temperature, S02 is found
to appear at 295-310oC, depending on the content of the readily
inflammable Fe and Cu sulfides. The OR-versus-temperature
curves reveal three maxima corresponding to fully defined
periods of sulfide oxidation. As the temperature is increased
(to 550-9000C), the maximum, OR rises sharply during the
Card 1/2 first 15 min. Thus, the time OR of concentrates presents a

SOV/1 37-58 -7-14079
A Study of the Rate of Oxidation of Lead Sulfide Concentrates
maximum at 5500, yet at 7000 it becomes considerably higher and begins to
vary on a descending curve. At 550-7000 the degree of oxidation is deter-
mined mainly by the:OR *of Fe and CU Sulfides, The de,gree of desUlfUriza--
tion in 15 min at these temperatures is, depending upon the composition of
the concentrate, 52-720/o. The effect oi individual sulfides is ielt at these
same temperatures. At -7.00oC, partial fusion and sintering of the concen-
trates begins. At 850, 900, and 10000 the total OR is determined by the
conditions of diffusion. As temperature rises from 850 to 10000 It increases,
the concentrates with the hi-gher galena and pyrite contents having higher OR
maximums than those with higher Zn contents. Simultaneously there is an
increase in resistance to diffusion, and this results in lower rate values and
a decrease in the overall time:GR. - The OR is aifected by the influence of the
chemical and mineralogical composition of the concentrates. Thus, at low
temperatures, the gangue rock acts as a catalyst, while at high temperatures
it inhibits OR. An investigation of the phase transformations shows that Pb
and Zn oxides are the fundamental forms in the products of roasting of the
concentrates. Rise in temperature carries with it a rise in the amount of
Pb and Zn oxides; the higher the temperature, the higher the juantity of
bound oxides. 1. Lead sulfides--Oxidation 2. Lead sulfides--femperature factors
1. Lead sulfides--Sintering
Card 212 A. Sh,

)/T,jLD POITOF. V - D
Sottio the,-r,-,,,l rqta on thn SIN-YOO-Cf-0. Vns~ All K-t~a,0 so that in (1) it holds,
F 2
(p) %j (p) P
r a to k(P) k(p
where P k( p) are polynomials and the functions tq) can be
continued analytically in the whole complox w-plane with the
exception of the out
(2) Im w = 0 Re w>m.
Besides the ~k(w) i.n all points w being distant more than
Card 2/3

A Theorem-a-the Analytic Continuation SOV/155-56-3-6/37
of Generalized Functions
from the cut (2) are bounded by a polynomial the degree of"
which does not depend on 6.
The author mentions S.L.Sobolev, and K.I.Babenko.
There are 11 references, 4 of which are Soviet, 2 Fr~,~noh,
1 Italian, 2 American, and 2 Swedish.
ASSOCIATION:Matematicheskiy institut imeni V.A.Stoklova All SSSR (Mathemati-31
Institute iemni V.A.SteklovjAS USSR)
SUBMITTED: April 16, 1958
Card 3/3

68022
46~_* 1 ~'4500 SOY/155-58-6-23/36
AUTHORt Vladimirov, V.S.
TITLEI an Integral Equation Which is Connected With Spherical
Functions \-A
PERIODICAL: Nauchnyye doklady vysshey shkoly, Fiziko-matematichaskiye nauki,
1958, Nr 6, PP 142-146 (USSR)
ABSTRACT% Let a and s' be points of the unit hypersphere -a ,
/- - a - a' the cosine of the angle between the directions a
and 0 . In Z_Ref 1 7 - Z_Ref 7 7 it is stated under different
suppositions on the-function KT/,) that the eigen values of
the integral equation
(1) rL - A - T(s)
are connected in a certain way with the hyperspherical functions.
In the present paper this connection is extended to the case,
where K(,A) is only assumed to be summable according to
Lebesgue.
Card 1/2

68022
On an Integral Equation Which is Connected 7ith SOV155-58-6-23/36
Spherical Functions
There are 9 references, 1 of which is Soviet, I American,
4 Hungarian, and 3 German.
All SSSR
ASSOCIATION: Matematicheskiy institlitlme'ni V.A. Steklova (Mathematical
T-n,q+ifiitP( imp-nialr-1- Sialclay AS 112SR)
SUBMITTEDs June 20, 1957 (Uspekhi matematicheskikh nauk)
October 24, 1958 (Nauchnyye doklady vysshey shkoly. Fiziko-
I
matemb.ticheskiye nauki)
Card 2/2

AUTHOR: Bogolyubov, N.N. and Vladjai=v, V.S. 38-22-1-2/6
TITLE: On the Analytic Continuation of Generalized Functions (Ob
analiticheskom prodolzhenii obobshchennykh funktaiy)
PERIODICALt Izvestiya Akademii Nauk SSSR, Seriya Matematicheskaya.,1958, V01,22;
Nr 1 , PP 15-46 (U-10
ABSTRACT: (x) which vanish
For generalized functions F
(x) and P
r
a
for x,,,'-o and xj;,-O resp., and the Fourier transforms
0
Fr(p) and Fa(p) of which are equal in a certain domain G
the authors prove the existence of a function of the complex
variables k t..., k which is analytic in the domain G and
0 3
0
is identical with Pr(p), Fa(p) for real pE G . This general
continuation theorem for generalized functions of several
variables is needed in the proof of the fundamental theorem:
Let translation-invariant generalized functions of four
vectors
,x x x ) i,j-r,a
F (X
P
l
2 3
4
be given.
Card 1/5

On the Analytic Continuation of Generalized Functions 38-22-1-2/6
Under traneformations L from the full Lorentz group let these
functions transform linearly with the aid of a certain repre-
sentat4,on A(L) s
AV,VI (L) F9; (X"..,x
P (Lxl , ... , Lx ) = E i
4 4
1 ,x
ra 1 3 2 4
F 9 - 0 for x x or x D ontains- al:l points
,.,too t a
2 off N2 1 Z x 2, 5 + V0 Z +
1 2 3 1 4 2
whe Z 5 4 4 2 2
. re -V is arbitraryreal 0 and .6 runs through the
interior of the ellipse
(1.3) A(t,V) + B(t,'D) cos + i C(t,-G) sing, 0 2r.
Card 3/6

05699
5-3/8
On Analytic Properties of Generalized Functions of SOV/38-23-
quantus Field'Theory
Here it is IV0 o 2
-1 If 2(t',d +,v0) + 2 0) - -1 2
4 1 4 Y (tIV+ V2 Bt
B -1 + 'e0) T (t' ~2' 'V + 'V02) +
2 1
+ 2 2 0)
G + vo) (t + Z
2 + (t, Wig 1
v + v 0) - q 2(t, -Y + vo)
2' 2 2
~
2 rti 140 2 +
v, 9 t + 'to) (t, 929 ,+ tj 2)- 4 2
C t 1 2
.2 2 ~rj + 0) (t 9 + -do)
+.I.%"(t' ~20 T +'r02)
2
where X2
(1-4) 1 2(t,V) _ (t + 0 .2 and
Card 4/ 6

5
On Analytic Properties of Generalized Functions of
quantum Field Theory
05699
SOV/38-23-5-3/8
(1 5) + (2M+,j-) (yI 2
2~t'j
2' ( 2/
0 M+/I-
if
2
+
KAI' 2 M+.a)

0
+ -I
4t
V(2t+ M

V F2t
+/W At2

The--,numbers M,,,,t~, vo are chosen so that > 0 for
v , -'e. 0 , t ;,> t
.
0
3-) For real (Pjvp21p,0 P4 from (1.1) p1 + p 2 + p3 + p4 - 0
for which the magnitudes 2 2 2
Card 5/6 ZI - P1 0 z2 ' P2 9 z3 w p3

05699
On Analytic Properties of Generalized Functions of SOV/38-23-5-3/8
Quantum Field Theory
2 2
% p , z belong to D., there holds the
4 4 5 - (PI + P2)
representation F ij(ply-op 4)
E 2 2 2 2 )2 1 1
Plf P2P P3 I p4 (p, + P2 P~7P3)2)
2 >
ipj - r,a for t - " 0
to and plo + p >
12 V p 3 30
Sobolev is mentioned in the paper. The authors use results
of Jost, Lehman Z-Ref 20 7 and Dyson Z-Ref 12 7 -
There are 21 references#-11 of which are Sovi;t, 4 American,
3 Italian, I French, 1 German, and 1 Swedish.
PRESENTEDt by N.N. Bogolyubov# Academician
SUBMITTEDs October 30, 1958
Card 6/6

iol
:44
A 6
Ila 3

VLADDIIROV, V. S.
"Primenenye metodov teorii funkey-i mnogih komplexsnyh
peremyenyh k differencyalnmy uraynenyam."
Report submitted for the Conference on Functional Analysis,
Warsaw, 4-10 Sep 60

35~~51 , -10."", 1 rj~; 2
s/o44/62/CJC 0, C C);~
c
ai
c
ul-, ju
u 2,
flu.
6
00,10
Val,
t
T)
C' C
the ns t'l rouJ-.
ru
i,,dLicp-te~; t in~ 21
the Ito
it vectors7
are U11
ca!!C1

cl i l/c".*,
t
Cn

I!C o n
k =4(p)
C
.
0 n

-ith to

rl
Set Ul)
j;jn

on

Such '.Inz~'-

if Z 1,L G 1,
u 11.1 )r
t evi~r.j
2. G(P, 0 r
ir, G t"cru holus
Card 2/4

3104416210C~r-/OC;2110~7 -/-/G.-2
on somu vtriational -rincidlez; . . . c 11 l/c4,,
dp~ >- C
0 'L 0
vili~re P,, are Lcj~;crdru~ respvct tu the ri~;ht '~-rd of
~1) cmc-suji.jcj~;i~L that F(- 1-1 = L2(SI X G, a~ P)). Some of
'le it 'r:;ld:i: L*= U;LU, t*-c U
ti
Uf(.-;, P) = f(-s,P); ti-le c.erz~tor
i v "16 c t o r L 5 i s c c, a. c t ir nd 11:. k~ t r i s Z~.efr:~::
!aft by the operLLtur S. T,',e r--i,ervalucs Of L-l~ -if
LLre its cil~enfunctions, then the syLtam S, i sc o.%, t c 14 rt L'- r.~ r LL nE.,
k
o
Further thc equation L 0u - ASu F(s, P), where L 0 )2 + 1
with the bo~ndv.-.-, concitlon
u 3, CA. 6rad U) 0; p (3, n) C)
CL3rd 3/'r t

On Cl 1 VC44
is considered.
I I tl 10 4' -UL!fri j,
C 0; il~ eC tL~ d 'U, t'l(-- ri - L !OLS
U + 11.11d U)
2
umier the conditions (2) and ~~), espccially the ei,,-unvaluDz of the
~yo problems are identicL.1, ahere as the eiGr_-rfunctJon,_ ~~.re connccted
u v
b~- the rk-lution above. ~'he oper&tor L is positive-31%, (lc~finite.
.1ccord-in Fvviedrichz~ cne ::iay the snace i vith Lhc
0
..e
'tric L-u (L u, v). F L) r
::.L v
a variatior-L-1 princi-,)I, -;iich 'uy the V4i~y iS L_ _(_~qLlt.:nCC OL
theo:L-erls. It is tlu_t t'lae condit-Lono (7,) z~re naturzl. Swj~.rzi_7
considt-rations or. the alp;:-,lic~Ltion of spherical 1,i~._rmonic_, Lo thc.,
up-proxim,ative _,olution of' (1), and on thu applicability of t~c 2ub:io,.,-.
Galerl-in.mctlwu are carried out.
JAbztra,`6tcr's note: Complete translz-.tion.1
card 4/4.

Double spectral representation of Yeymaa amplitude for a diagram
of the fourth order. Ukr. mat. zhnr. 12 no.12:132-14,6 16o.
(MBA 13:10)
(Ihmetional analysis)

If..-2100
AUTHORs Vladimirov"V.S._
--=W-
TITLE: On Approximative Calculation of Wiener Integralsj~
PERIODICAL: Uspekhi matematicheskikh nauk, 1960t Vol- 15, No. 4,
pp. 129 - 135
TEXTs The author considers the Wiener integral
M I - ~ F(x)dwx
C
where C is the space of continuous functions x(t) defined on (0,1), x(0)-O-
An approximating formula for the numerical calculation of (1) is sought in
the1orm
00
(14) F(x)dwX IL " k F(xk)
k,_00
where Xk and xk( t) are chosen so that in the following cases (14) changes
Card 1/4 . X/
S/042J60/015/04/03/007
C111/C222 82227

On Approximative Calculation of Wiener S/04y6o/015/04/03/007
Integrals C111 C222 82227
to a strong equation% 1) for all odd functionals F(x) - - F(-x), 2) for
functionals
+
(4) 1V(X) - K0 x(tj) ... x(t,)dt Vot 1~' (t1'...'t.A
Y
0 0
where 1. are arbitrary functions of bounded variation, 3) for functionals
(12) F(X) jjx 112 1 1 x(tl)x(t2)d 2
0 0 t1)t2 6~'(tl'td
where 6' is of bounded variation and
(13) x 112 2(t)dt
It is stated that these claims are satisfied if
Card 2/ 4

On Approximative Calculation of Wiener Integrals B/042/60/015/04/03/007
C111/C222 8222-7
1(28) k 2 (2k41)2 + 16
(27) T.
k +
FT 7F(2k-71
xk(t) k ack(t), k ~ 1,2....
(8) 1) zt, Ao = 1 - 8 2
j Z sin (j - 7
k-1 T. (2k-IT+ 16
Theorem s Let the functional F(X given on C be continuous, i.e. from
11 Xn - X0 11--*0 there follows F~x n)---> F(x0 Let exist a positive mo-
notonely increasing function H(n) so that
I F(x) H( 11 x 112) x G C
(37)
and
Card 3/4

On Approximative Calculation of Wiener Integrals S/042J60/015/04/03/007
C111/C222 82227
(38) H( + 11 x 112) dwx < 00
for a certain >-1 . Then it holds
4
(39) lim I n F(x) d w x
n --3100
The author mentions N.N. Bogolyubov, D.V. Shirkov, I.M. Gellfand and A.M.
Taglom.
There-are-7 references : 3 Soviet, 3 American and 1 Swedish.
SURITTEDs February 10, 1959
Card 4/4

88202
S/020/60/134/002/027/041XX
/4-400 C 111/ C 333
AUTHORs
TITLE: Construction of Holomorphism Hulls for a Special Kind
of Region
PERIODICALt Doklady Akademii nauk SSSR, 1960, Vol. 134, No. 2,
pp. 251-254
TEXTs Let Rn+1 be the real space of the points x =(x 0, x 1"""xn)
(x0, 1); p, q its points; C n+1 R n+1 + i Rn+1 the space of the
2 2 2, 2
p + iq; ~~K X X - X x
2 j2 0 jxj, 0
1X1 x0+ Assume that r+ :nd F_ are the cone of light to come
(X0> ), and the gone cone of light (x 0 < - 15E I ); r-= F+ u F-'
A smooth curve is called time-like, if its tangent vector belongs
to A smooth surface is called space-like, if its normal belongs
to The linear continuou 's functi.GraLs over the space S of Schwartz
are called generalized functions. :,siiume that S* is the space of
the generalized functions, which is conjugate to S. The generalized
functions F+(p) and F_(p) are called delayed or leading if their
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2
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Construction of Holomorphism Hulls for a Special Kind of Region
'~'(x) and (x) vanish oukside of T + rd
Fourier transforms F
respectively; f(p) is called commutator, if f(:z) = 0 for x < 0.
A holomorphic function F( ~ in T' (or T-) is said to belong to
the class N+ (or N_), if 1.~ for arbitrary qC- [-+ (or f--), e > 0,
t -, t
> 0 and a certain real 1 only deponding on F it holdst
0
) e F-~ t(1 + I p I )l ; in SO there exists
~F(p + itq) I < e (q, E , t
0
- 1 0, D)) of the
the boundary value F(p
+ 1 0, D (or F(p
o
o
function F(p + iq? for q 4 0, q e f-+ (or r--). Let N = N+ n N_
The function F(~ ) of the class N+ (or N-) is called analytic
- i 0, _j). Assum-a that G is
continuation of W + 1 0, T) (or F(p
o
an open set in R"* 0 and le the complex neighborhood of G with the
property that, if a sphere of radius I belongs to G, the correspon-
ding complex sphere of radius 0.11 belongs to G.
Theorem 1: In order that a function F(S ) holomorphic in Tk-/ G of
the class N exists, it is necessary and sufficient that its
- 1 0,
+ i 0, _ff) and F(p
boundary values Fi(p
o
0
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Construction of Holomorphism Hulls for a Special Kind of Region
1.) are delayed and leading functions respectiviely, and 2.) coincide
in G.
The domain T \j G in theorem 1 is not the holomorphy domain; F is
holomorphic in the holomorphy hull E(T%~Z). The domain , where
F(p + 1 0, ~) coincide, is the real section of a certain holomorphy
dom9i;i.
Theorem 2z If the commutator f(p) vanishes in a domain G, then it
also vanishes in the smallest convex hull Bo (g) of the domain G
with respect to the time-like curves.
Theorem 3: Every function F(j ) of the class N which is holomorphis
in T v G where G is an arbitrary domain, is holomorphic in the
domain H~T \j-G) which consists exactly of those points ~ for which
every complex hyperboloid (f I _ u)2 = a (u, s real parameters),
going through possesses at least one common interior point
with G.
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The author thanks N. N. Bogolyubov.
There are 14 references: 6 Soviet, 3 French, 4 American and 1
Italian.
ASSOCIATION: Matematicheskiy institut imeni V. A. Steklova Akademii
nauk SSSR (Mathematical Institute imeni V. A.
Steklov of the Academy of Sciences USSR)
PRESENTED: May 3, 1960, by N. N. Bogolyubov, Academician
SUBMITTED: April 27, 1960
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AUTHORj Vladimirov, V.S.
TITLEs- Properties oi H-o-lo-m-orphism Regions a A lied to the Study of
Solutions of Differential Equations X~ pp
PERIODICAM Dokiady Akademii nauk SSSR, ig6o, Vol-134,NO-3, PP-511-513.
TEXT: The author uses the notations of his preceding paper (Ref.1).
Every linear continuous functional over the space S of Schwartz is called
a generalized function. In S* the author considers the equation
(1) U(p) * f O(p) - f (p), f E S,9f* fo G 0 0,
where
r4
(2) f(x) - 0, 0
2 0
for x2 ~ x ^& ;(p)9
_X2