SCIENTIFIC ABSTRACT MIKHLIN, S. G. - MIKHLIN, S. YA.

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• Collection: Scientific Abstracts
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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

0. On some ectimates coanetted wit regn!l_
-

TundiR 443~
rOnS. Woklady ad. Nauk SSSR (N.S.) 81
i
1931
n)
(R
46 ( a
uts
).
Ul'x& be 8'.mi-volued continuous function de-
the 06sed -init circle 0+0:111g.
fincd on
,
Ish" on the b0 dilry x1'+$O_1 , and
~tu ax I ~a
alu X~l I f Intqrabla aqvAre on xj~+Xo'~ 1. It
~
t
OWn
ha
here_
t t t
dsbl a real numbei 0 such that the
-
.
ual, -
in
IT ity
:ff +
ff

w
~herek-l miction a.
--Th Se 0
0 06ormakes it
f a formula of F. Tricoval [fdath Z
27P -1331- (101)] for differentiating Cauchy pr1njv;i
ue intV
W i gals and of a previous theorem (if the author
CC
R--(Doklady)Acad.,Sci.URSS(N.S.)IS,429~432 '(1937)1
Uvpehl Matem, Nauk 3, no. 3(25), 29~412 (1948)
,
fated _. as Amer. Math. Soc. Translation no. 24 (19S0); these
RtYJO, 305; 12, 107] concerning integralsof this mr.
J. B. Diax (College I
no
1 eve
#
&the t 04
Bo

I - ~ I r~l I I - I N/, , ,-,. -
PHASE I TREASURE ISLAND BIBLIOGRAPHICAL REPORT AID 712 - I
BOOK Call No.: AP476493
Author: MIKHLIX, S. G.
Full Title: FRORM OF A NININUM OF TM QUADRATIC FUNCTIONAL
Transliterated Title: Problema m1n1muna kvadratichnogo funktalonals
PUBLISHING DATA
Originating Agency, Series "Sovremennyye problemy matematiki"
Publlshlng House: State Publishing House of Technical and Theoretical
Literature ,
Date: 1952 No. pp.: 216 No. of copies: 5,000
Editorial Staff
Contributors: Gelfand, I. M. and Shapiro, Z. Ya.
PURPOSE: This book is Intended for the young scientist who works In
the field of mathematical. physics.
TEXT DATA
Coverage: This book is a summary of the scientific reaearch In the
theory of a minimum of the quadratic functional in Hilbert's
space, most of which has been done by such Russian scientists
as Mikhlln, S. G., Sobolev, S. L., VIshn1k, M. I., and
Eydus, D. M. This book is divided Into four chapters;
Chapter I, Formulation and Solution of Variational Problems;
Chapter II, Some Auxiliary Information; Chapter III, Applications
1/2

I. KEKHLIN9 So Go
2. USSR (6oo)
4. Science
7. Experimental methods in organic chendstry. Pt. 2. Pervod a nemetskogo. Moskva# 1952
9. Monthly List of Russian Accessions, Library of Congress, Januaryq 1953. Unclassified.

NJ-V'HLIN 5 G
ussR Wo)
MAritle Plates and- Shells
Determination of the error in cos"tIng an elastic shell as & flRt PlAtO.
Prikl. mat. i makh. 16 no 4, 19;Z.
9. Monthly List of Russian Accessions, Library of Congress, November _195A. Unclassified.
2

MR/Pbyaice - Elastic Sheila U Jun 52
"Certain Theorems in the Theory of Operators and
Their Application to the Theory of Elastic Shellaft
S. 0. Mikhlin, Leningrad State U imeni ZhAnnov
"Dok Ak Nauk SSSR" Vol LXXXIV, No 5, PP 909-912
Considers a Hilbert apace 3 and a conjoint opera-
tor A pos in N. Constructs a new Hilbert space
RA as the act of regions D(A) in the metricL/ Z, 6
a (Au,v), /u/2= (Au,u); here certain of the ideal
I.ements of pace HA can be identified with
:
uitably cho:en elements from H: If u. is an ideal
element of HA a sequence un in D(A) exists such
22W94
that lim/un-u /=O and lim/un-uc,/-O for m,nsoo,
-Yiy u with the limit toward which
than we ident
the sequence (un) ?ends in the metric of apace
1. Shows that such a law permits one to identify
u0 with not more than one element of B. Sub-
mitted by Acad V. I. Smirnov 8 Apr 52.

x1flOn, S, G, A' Anceralug a thro~c~m Olt 6itlEdness of a
11-Ta-g-MIPM egral Opersiticir, -Unwhi Mallem. MIA (N Li".) I
8, no. .1 (33). 213 -217 (1953). (Russian)
Ina previous expository work (1] [Uspehi Nfatem. Nauk
(N.S.) J. 3(25), 29-112 (1948); these Rev. 10, 3033 flic
autbor matle use of his earlier theorem, accnirifing to whif Ii
a singular integral operator is 1xitillufal in L, if i(ff 9$~Mlifjl j-4
lioundcd. The author rendem greater precision to this
dicoreni, importint ill view of some of its ircin".juviiii es.
The notation is that from (I]. If the symbol of fhe sullph.%l
singular operatnt- depends only on 0 and is 1~)undcql. flit it
the norm of the operator in Li(E.) dtles not exrVi'd flic
maximum of file mollulus of (fie operator. Whence. it flit-
syrullol of the simplest singular opermor is (if Ow Itirm
En.(Alo),N(O) and the scric-; x- E utax In.(AN)l max 14,.(0)l
Mlthorritiottl Roviams cmiverges, Own file opt-rator is Nnintled ill 1.101"..);11141 if-.
Vole 14 How 0 noriii is 6s. The opvrator (2) An = -f01.. OW, ,

Sept; 0 1953 k bmindrd ill L.(I-',) if flit, (haracli-ri,lic f0l.,Oi Irt,
dvriv.iii%-v,;wiih rt-,Iw,ct toetif tivlf-i
aiiii i-f

too, C
Flit. fit ti-Olim- if -m; tilar ifil, -.-ral -I,- i11"I

If* J."t

21 59T(k
TMSR/Mathematics Functional Analysis I M&Y 53
"Application of Fiinctional Analysis to a Slanting
Elastic Shall Having the Form of an Elliptic Pa-
raboloid," V. S. Zhgenti, Gorl State Pedagogic
Inst im H. Baratashvili
DAN SM, Vol 90, No 1, pp 9-11
Solution by functional analysis of the eq of equi-
librium of a slanting shell derived by S. G.
Kikhlin (Priklad Matemat i Kekhan. 16, go 4, 417
(1952)). The solution consists of expressions that
converge according to S. L. Sobolev's inclusion
25W66
theorem of spaces (Nekotorrp Primeneniya Funk-
tsional'nogo Analiza v Matematicheskoy Fizike,
Some Applications of Functional Analysis to Mathe-
matical Physics, Leningrad, 1950). Present" by
Acad S. L. Sobolev 23 Feb 53.

r-'U a DT IL OL
ft solookft d a
*My& *Pad=& r%&f- ir Ak";,l -IF
91, Y23-736 (1953). OWmARn)
C I
=iidff IL SAIIIS OMO -t 0 ~~ id ft haV-plam y>o,
whom bouoda~romflits ofailulto Ulterval (6, b) - r,
tho x-4xk arA of a curve r lyWg In y>0 mye &Dr its ermi-
q~ pants at a and 6. Let AG and Mo he two sets of functims
wbl& are twice cant k
contlnuoWydiff
lab oatheclosedoet!
J Uo+r+rl and vaniph, on r. The functfmg [a irt also I
Vt

IVIIIIM W r WIN& t1lass a Mt theiryderivadvas e"d,
to sem ost LI. Suppow the finmd= Ify) f& cmd 4a'
idw fnftrvd 0 SyS V. wbew F k greaser thaa or awal to'
the --f-unt ordinaft *( the pobts of the curn r; thAt
r f(0)-0.- aid 1(y)>O whtit y>O. The differantlal operator
of (UM-
OW tim atts
,
C
doesVt s" Us, pMom two opmt^ wW& #W be
''denoted byAt and At, respettiv*. The Gist them= states'

that At avA At am both
posMve defialte ova tha HUbert
Ls(Q). (L ft. then ezkt positive Wastantt y'r =I&
v) for i-L. k and any a Ea L%(Q)j.
i This fact pennits the 4ppReation of v"doad medwds Cd.
Mthlin
Problem of the askdmuza of a quadratic fwzdcW,
Gostehttdat- Wsecw-Lenlagmd, M?; tbtw Rev, 14, 411
to th6 bouadary-vabje prohkxv tir4r of the partial
diffemtial equatiom -f(y)0g1W-61v1W- p(ry). with,
IF In rj(U). subjeLt-to either die- beuwlary o=&tkwI
UIr-D. Llfr--O; Or 91 P-0, srf r,-O; and Also to theco"W
"dfair bmndar~-vafue problem with ths homagentous
I equaticit and non-homogentous boundary condWom Fur-!
ther ~Itz wncera the cAse wim -y-., ). w m
(y (y he
a(y)?.k>O for 0:5yrV and cr>O. aqd the diffetentiall
r
opena~o

)
6Y
r. ir. IN4& (Collep Park, hfd.).

I I Au,
53
7";u I
Int- --rF-, Ion of the Poicson Equ,-iti )r-. in nr. Inf I -.I' - Pe,:i )r., "S. 3. Yi~--
nAN SSSR, Vol 91, 'Tr) 5, p-p 1O1e-lC"7
CY rncteri,-.es the ei,- -en rolutic,.,,9 f.-:)m thc tYe PoiEsm e, -au= f(x)
(f in L2(C)) in Pn i.fir.'Ite m6ij.,. 0 )f the m-di.-nensional Luclidert.i a-~.qce, f~)r the
boundary coiid!ti-,n tx/c,;= 0, where S the Ooun~.,.:-y of this rt;Li)n lieu in - f'-At,
-,f the spnce. Pi spnts-d by Acqd V. 1. S! irnov 29 *-IqY 53.
z66T87

MTKYLTN' G.
U'39RA'athematics -Bgundry-Value
Pr,-) b 1, e mn
11 Sep 53
"Theory of General Boundry-Value Problems for Elliptical Differentibl Equations,"
M. 5h. Firman, Leningrad Mining Inst
DAN SSSR, Vol 92, No 2, pp 205-208
Discusses certain problems con!.ected with M. 1. I:isik'F theory of -enera-1
boundry problems for elliptic differential eqs (M. 1. Visik, Trudy Mosk
Met Ob-va (Works of Voscow !bath ~,oc), 1, 1952). Limits the -iincussion
just to the case of the self-ad.4oint lifferential operator wl-, ch -til.zoa
the Important re-ults of M. G. Kreyn (Yatem -hor (Math Eymposium), 20((~2),
3, 1947) in the invest1wation. Cit .9 relt-ited work of ". Vikhlin
(Problema Minimuma Yvadratichnogo :;'unktsionala, 1~)52). Prp-ented by Aoad
V. 1. 7mirnov 10 Jul 53.
269T72

14DUILIN, S. G. , Ed. N/5
613.054
Nekotoryye voprosy teoril raspros-tranenlya voln v odnorrejnykh I
izotropnykh sredakh, organichennykh ploskostyani ('certain 1:rotlems r)n
the 'Meory of the Expansion of W ves in Uniform ani Isotropic
Environments of Limited Planes) Leningrad, Izd-vo Leningradskogo
Univeraiteta, 1954.
222 p. (Leningrad. Uni fersitet. Uchenyye Za,-,iski. Seriya Matema'iches-
kikh Nauk, Vyp. 28)
At Hend of Titlot Dinamicheiskiye Mdachi Te-rit Uprugosti, 4.
Bit-liography: p. 221.

HIMILIN. S.G.
Degenerating elliptic equations. Yest.lon.un. 9 no.8:19-46 Ag 154.
(Differential equations, Partial)

U,g S I
Oa the thaoxy of degenerate altfp* eqda-.
-----

7 dom Do
Zady Akad. Nauk SSSR (N-5.) M-185
-
19S#
R
i
uss
an)
)-
(
(
4 The author considem. the differentiAt equation
(A
M& it of efflptle type [a a bounded domain Q of Euclidean,
space; the ooefficients A,* are supposed wffcimtly regutar.'
a is supposed to be the sum oft finitt number olstar-shaped!
-idordalintopermittheikAicabilityoldii:lWus&xtdm=',
of S. L Soboley C-Same appikations of functionat analysis;
to mathematkal physim. rz&t. Uafh~ Goa. Ualv,

Al 4,
~~ 1 1930; then Rm H, S65]. The degeneracy of L consists Em,

'
e the edsten
Ce of At proper subftt of the bounduy r of a
' such that on th;t subset some of the ekftWueg of. the"
autrix [Aal , am zew. The prwat note Is coamned with

the formulat .
ion, of'spectrat proper6ei, of the, operator L:
Olarlir ya didws and two types. of de-'
genemcy. Some of the results have Skawy been announced
"for 0-2 Lrt the papee'rtyiewed above. r. Dr. D(GL

~Aw
'
'
. 11 (1956)
Vestnik Leningrad. Uhiv
no,
is concerned e

gular operator A
Tid .,with th sin
Paper
given y.
b

Ap(x) a(z)#(z)
4f

eld the e
-:Wh x4fid uiivedom 41. udWah ~s-spaces R., 0

tha
is Ogle IxtWeen x 4nd ~t-j, r is th~ dist4tice, between
'
n egra s-
hi th
I I tak elletiso 61 a. r~rlncipal.
on

I 'the author givf-s Improved
v
a it prools of bii previoUs
-

resufts on the regulariv~bility'of-
n e behavfqur
A A don ih
:-:Of A 2:sr-an, operator on j.
In the coneluding' pam hs th thor makes some
r b~*&Clei eau
a
conune
mu
t 6ft and Z
d
jTra6s
.
n
a
pe
;
yg
:
?
C
'Artery - Math
78 (1955), 209-224~ AM 16,- 816).
''

an
Prokss~ir Z;i
Mund informs me that there Is. actually
'
,
which is I ow-
~:oversight on p. 213i line 12 of the pa
per

ever not diffi~
ult to correct without changing the essential
'd - f I U The rrection appears in Trans. At
I C.1 0 t le Proo c0 ner '.
Math, Soc. 84 (1,957), 559-560 [MR 18, 894). Meanwhile A
comPlettly different proof -of a more general result was
publishrd by C.Aflerftand him (Ainer. J. Rath. 7$ (1956).
:289-309, vsIllocially p. 290.,Th. 2: MR-18, 8941.
N, rj
Kohn (Priurt-lon
J
J
.
.
,
,

14IMILIMP S*G*
On Ritz's method. Dokl.AN SSSR 106 no.3:391-394 Ja 156.
(NUU 9: 6)
l.Laningradakiy gomdaretvennyy universitet imeni A.A.Zhdanova.
Predstavleno akademikom T.I*SmirnoM.
(Spaces, Generalized) (Operators (Kathematice)

C , (.r .
L INI ~)
SUBJECT USSR/MATHEMATIC3/Fourier serlas CARD 1/1 PG - 572
AUTHOR MICHLIN 3.0.
TITLE On the multiplicatorn of Fourier Integrals.
PERIODICAL Doklady AkaJ. Nauk 12L 701-705 (1956)
r9viswad 11/1956
The theorem of Marcinkiowirz StulAa Math. 0, (1959)) on the multiplicators
of the Fourier series is formulated by the author also for complex functions
and multiplicatora. Besides an analogous theorem for Fourier Integrals lo
proveds Lot (~(x) be continuous In the whole E. (at most with exception of
the origin) and let its derivative dm ~ /a xi. .? XM exist in every poInt,
while all preceding derivatives are continuous. Besides l*tjxjk IDk( 1!~ 9
ic-O,1,2,..-m (Dk an arbitrary derivative of the mentioned ones,, k 1 5 order).
Then the operator
F(g) - 'I -F2 91(X.Y) ~(Y)dy 9_1(y's) g(z)dz
(21() f
sm Em
is defined on a set which is dense in Lp(Em), lw-P.4oo. Furthermore the
operator is bounded in this space and IF 114- Apim M. where Ap9m Is a conetant
only depending on p and m. From this theorem the author concludes a now cri-
terion for the boundedness of a singular integral operator in Lp(Em).
IHSTITUTIONt University, Loningra4.

L I N I -) L!,
PHASE I BOOK EXPLOITATION 155
AUTHOR: Klkhlin, S. G.
TITLE: Variational Methods in Mathematical Physics
(Variatsionnyye metody v matematicheskoy fizike)
PUB. DATA: Gosudarstvennoye izdatellstvo tekhniko-teoreticheakoy
literatury, Moscow, 1957, 476 pp., 6,000 copies
ORIO. AGENCY: None given
EDITORS: Akilov, 0. P.; Tech. Ed.: Volchok, K. M.
PURPOSE: This book will be of interest to scientific workers
In physics and engineering. The author's intention
is to acquaint readers with "variational methods* as
applied to mathematical physics, the theory of elas-
ticity, fluid mechanics and to other fields of engineer-
ing.
COVERAGE: This book is a revision of the author's "Direct methods
in mathematical physicau published in 1950. In th13
Car4z:Aj~

Variational Methods In Mathematical Physics (cont.) 155
revision the author is primarily concerned with variational
methods, namely, the energy method, the method of least squares,
the method of orthogonal projections, the Treftz method and the
method of Bubnov-Galerkin which Is closely related to the energy
method. One long chapter is devoted to methods of determining
error bounds of approximate solutions arising In the energy
method and in the other methods. This problem was only mentioned
in the previous book but is treated here in the light of recent
foreign and Soviet work. The numerical examples were reduced
but those included carry calculation to the determination of error.
One chapter presents the basic tasks of mathematical physics
introducing the concepts "operator" and "functional" and analyzes
the most common operators of mathematical physics. The theory
of eigenvalueB is investigated in connection with various problems.
In addition to variational methods some finite difference methods
are presented. Reference is made to V. I. Smirnov's "Course of
Higher Mathematics" and the author thanks K.Ye. Chernin for
making the new calculations In the book, and 0. P. AkIlov who
reviewed the manuscript.
Card 2/1.1

Is and c,iltiple eirgular Integr
t. MU 12 no.7:143-155 #57.

4A U THOR 1 ('14 2
-----------
ITLE Singular Intef~rals in tlc~ S~aces L
v prostranstvakh L p ) p
PERIODICAL: Doklady Al~ad.llauk SSSR, 1957,%'01-117,Nr
ABS'11'RACTs In the Iresent papor the author uses the -., *ati,,,is fr,
Lh ef.1,2 which are r.ct available for the rr-vip-r,,r, -~,, i-h -rnclerq
difficult the understanding of the ~nper.
Theorem 1 1 If the symbol P (X,O) of ths~ 9 nl-ilpr .-,- -at, r
Au - a(X)U(X) + f(X,Q) u(y)dy
rm
and the derivatives M
2
M-,
are continuous for fixed x and ~,-unded indrpr~ndpntly f x and
if the generalized derivative
M 2 M 1
rd 1/3

riL- lo- (/4
,ular Intearals in the L;paces L p
,mista and satisfies the inequality
M-1 I
d
J., or 7-2
m M-T
where 1 p < 00 , then A is hotintled i r. L(E r 4
r, 7
Theorem 21 Let the sinjular inteCral Prjuatirin
A u - a(x)u(x)+ f(Y'Q) U(Y)dy+Tu = e(x) '-"X)E L ~E
M
r, r
m
be Civen. It is assumed that T is com7letely c(,ntinuous in
Lp (Em), that the symbol A 1 satisfies the ~onditiona of
theorem 1 and vanishes nowhere, that a(x) and Cl-,G) satis-
fy the inequalities
la(x)-a(y) < Mry(l+lxl 2 r p + I.Y12
2
f (x, 9) - f (y, 9) _< 1r)f( 1 + Ix Im( 2_p 2 ~1+ 1.,2 2
Card 2/3

Singular Intef;rals in the Siac- I. P 20-1-(/142
-fYipro IA ari,l T- ri
Th e n A 1 iov r, o r rw.~ ty,~ a 1; 1,, L.
Thporem s -Ii,~ A
L
f
Q 'ual 1% L, 'L
t' "
4 3oviet and ' foreign references are quoted.
AS:)'vC IA'.L'I 011i IAningrmd State Univprsity Im. A. A. Zhdanov (TenI-np_radzkIy
gosudaretyennyy univereltet Im. A. A. Zbdanova)
PRESENTEr: V V.f.Smirnov, Academician, May 20,1957
S-,-, Nl%v
AVA I LA B LE i L I '--a ry o ro!') f;

AUTHORs Mikhlin, S.G. SOV/140-5B-9-7/14
TITLE: ReZiks on o dinatp Functions (Zamechaniya o koordinatnykh
funkteiyakh )
PERIODICALs Izvestiya vysshikh uchebnykh zavedeniy. Matematika, 1958, Nr 5.
PP 91-94 (USSR)
ABSTRACTs Let A be a positive-definite operator (see [Ref 1] ) in the
Hilbert space H, and f an element of H. For the solution of
the equation
N Au . f
according to the method of Ritz certain coordinate functions
TV f2"" Yn.... are chosen and the approximative solution un
n
is set up in the form u. L a 0~,' whereby the a k are ob-
k-1
n
tained from the linear algebraic system L ['Pk"Pjl ak
k-1
jnl,2,...,n. If the angle between Tn and the hy-perplane
Card 1/2 through T1 ' Y2 ...... Pn-1 is denoted by at n, then for the de-

Remarks on Coordinate Functions SOV/140-58-5-7/14
terminant of the system it follows D det ',J]jj n
n - 11 [Pk k,j-l
r Isin2O~k. If D - lim D n is positive, then the exactness
k-1 n_~a)
can be improved by increasing n (reliable system of the
if, however, it is D-0, then the system of the ~Oi is unre-
liable, for largo n the application of the mothod is doubtful.
7-
The convergence of OD cos266k is necessary and sufficient for
k-1
the reliability. It is shown that an orthogonal normed system
is reliable and therefore is more suitable for the application.
An example is given.
There are 2 Soviet references.
ASSOCIATIONs Loningradakiy goeudarstvennyy universitet imeni A.A.Zlidanova
(Leningrad State University imeni A.A. Zhdanov)
Card 2/2

89545
16 inn 0 C111/C222
AD OR: *1khlin, B.G.
TITLEs On the solutions with a finite energy for elliptic
differential equations
PRRIODICALs ReferativM7 xburnal. Matematika, no.0, 1960, 98,
abstract no. 8923. Uckr. sap. Leningr. gos. pod. in-ta In.
A.I.Gerteens, 1958, 183, 5-21
TZXTs As it is well-known, the solution of the equation Au. w f, f EH
(H -- a certain Hilbert space, A -- a positive operator) is equivalent
to the determination of the minimum of the functional F(U) -
(Au9u)-(u,f)-(f,u). In the region of definition D(A) of the operator A,
a now metric can be introduceds (Au,v) - ju.vj; 'Lu,ul -Jul. By com-
plating DA in this metric one obtains the now Hilbori apace HA. If the
functional (u,f) is bounded in HAthen there exists a u0C- SA 16Y which
the functional F(u) gets its minimuml in the present paper, such a
u0 Is called a solution with a finite energy. If A la Ro positive
defin.ite operator then In general uor- H, As an example the author
conaiders the problem
S/044/6o/ooo/ooa/o17/O35
Cdrd 1/2

8954.,
3/044/60/000/008/017/035
On the solutions with a finite-, CIIII0222
6u - f W. x C. (.- I ; U~' m 0
(Clio an infinite region or the m-dimensional Euclidean space bounded
"my the closed surface J" ), Here the 13 Pace HA is the set of functions {u)
satisfying the oonditionst I) uc-- WO )(01 ), where.0 L a an arbitruy
2
finite regionj 2) grad uEL 2(Q'); 3) Ulr' 0 in the sense of S.L.Sobolev
or R.Courant. It is proved that if f(x) - div P, P4 L 2# -7 'Y FE L2 then
4xk
there exists the solution with a finite energy and has generalized
second derivatives which are quadratically summable in every subregign
of R . Parthermore it is shown how these,results can be generalized to
an equatton with variable coefficients, to the Poisson equation with the
boundary condition ~u/ 3,) + 6ulr - 0, and to an elliptic equation with
variable coefficients (in the finite region) which degenerates on the
boundary.
Abstra,dtor's notes The above text is a full translation of the original
l
oviet abstraci.]
Card 2/t2

KIKHLIM, Solomon Grigortyevich; ZMER, I.Te., red.; POLIGEATA. R.G..
-tekhn.red. -
(Lecturee on linear Integral equations] Lektaii po linainym
integrallnym uravneniiam. Koakva, Gos.izd-vo fitiko-matem.
lit-ry, 1959. 232 p. (MIRA 13:2)
(Integral equations)

GMT %nit I a a
OTAIP floalaziul PuT :Puvlmo 30spupdop
30 mm jo ruct3natiasid
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4LIVA'02 sO-.:-VL1D1JXX low I Wfu (0)91

ALSKSAIMROV, A.D.; AKIWV, G.P.1 ASMIEVITS. VALIAITMR. S.V.;
VLIDIYJW-V, D.A.; VMIKH, B.Z.; GABTPIN, M.K.; KAIM01OVICH, L.V.;
KDOINA, L.I.; U)ZINWIT, S.M.; lADTZH9NSXATA, O.A.; LIMX. Tu.7.;
LXRRIXV, N.A.1 V=Xo--Qf'G-~-,--YAlrARDV. 3.M.1 VATANSON. I.P.1
NIKITIN, A.A.; POLTAKHOV, N.N.1 PINSKE-R. A.G., SMIRROV,' V.I..
SAFROVOVA, G.P.; SHDLITSKIT, Kh.L.-, FADISYBV. D.K.
Grigorii Mikhailovich Pikhtengollts; obituar7. Vest. LOU 14 no.19:
158-159 '59. (KIRA 12:9)
(Fikhtengollts, Grigoril Mikhailovich. 1888-1959)

16(1 )
AUVTOR: !'oikhl in, S. G. SDV/20-12~-,!- - ~-f/74
TITLE: Two Theorems on Regular~ ers '~ve teoremy o regulyarizatorakh'
PERIODICAL: Doklady Akademii nauk SSSR, 1359,Vol 125,Nr 4,pp 737-7~~ (-JSSR)
ABSTRACT: Lot E1 and E 2 be Banach spaces und A 6(E 1-*E 2) a cloqrd operator.
B 4E (E2-*El) is a rogii1ar 7.ers --~f A if BA = I + T, wn-~r- I il
the unit operator in E 1 and 7 is e- -,-)mTl,-te1y continu-.i~ pe-:I*rr
in E The regul,,, zerg is called eq,i4val(,nt if Au
BAu Bf are equal for all fG 7- 2* Let all considered
be additive and homogeneous.
Theorem: If a clo3ed operator A nas a re-ularizors, ther, 1
operator is normally solvable.
Theorem: In order that a cloged operator ~ has an equivalo.'
regula izer it is necessary and sufficient that this npr~ri'
is normally solvablo and that ita index to finite and non-
negative.
There are 4 Soviet references.
PRESENTED: December 10, 1958, by "I.I.Smirno-i, Academician
SUBMITTED: December 9, 1958
Card 1/1

AU T'i~) R Mikhlin,3.3. 5 C 7/2 4
-------------
TITLE: Differentiation of Spries in 7r-rms of Spherica'-
FERIOLICA~: Daklady A?.ademii na-ik 2,T,~
ABSTRACT. Let 5 be the -unit sphere in the E-,iclldean E If x is a point
o f the Em 9 tile n 1p t I x X//9 L,-, t JL d eno t o a 3p,ie. i - a'~
I ay.- r Let every f'r&~ defined -,r, 3
3 1