SCIENTIFIC ABSTRACT KREYN, S. G. - KREYNDLIN, L. N.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000826420020-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: January 3, 2017
• Document Release Date: July 31, 2000
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT


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analft)r Moscow,, Izd-To "Natlra",, 196h,
42h p, biblioot indeico Err&t& slip ixiaertedo 17,.~500 copies printed. Seri"
no"Le.- 3pravochnay~a matemUcheskayu biblioteka.
TOPIC TAGS: funotional analysis.. mathematicsip operator eqnation., quantun
mechanics, Hilbert spaceo Banach space,, linear differential equatiou
EMILFCOE AND CCUFAUGEt This issue in a series of Handbooks of the Mathematical
Library contains much material grouped basically around the theory- of
operatore and operator equations. . It presents the basic concepts and rzthode
of Ametiontl analysis., theory of operators in Hilbert space and in conLml
sT~az3p the theor)r of nonlinear'oper&tor "tiona., the thcor7 of standard rings,
a-t;P1icd to equations in partial.derivativea, tointegral-oquationa, L
separato operator of quant= mechanics* Citing
of -the theory of generalized functions takes up a large part of the book, The
boolk explains mathematical factaS theorums and formulass as a rtzle,' are given
Card
1/2

L 45609-65
ACCFSS1Q.; uR o4o4373h
Uithout proofs, Main attention is' given to concepts ~dthout excessive detaile
The book Is intended for mathezaticiaw,, mechanical enducerat and phraicistaf,
It contaim much of value for aWdents and graduate atudentso
TABLE,0F CONMUS (abridgedlt
Foreword - 13
Ch, I. Basic concepts of Ametional analftis - 17
Ch. II, Linear operators in Hilbert-space - 79
Cho III& Linear differential equations in Bana'ch apace 146
Ch. IV. flonlinear operator equations' 187
Ch, V, Operators itt apaca with a cone 229
r1b IVI. CoMutative standard ringa 256
Ch. VII, Qmntum machanion opemtarB - 2791
Ch. VIII. Generalized ftnetions* 323
~Rihl lugraph7
babject Index
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MIMI, S.C. (Voronezh)
"On the theory of oscillations of a viscous fluid".
report presented at the 2nd All-Union Congress on 'Ibeoretical and Applied
Mechanics, Moscow, 29 Jan - Feb 6h.

KREYN, S.G.; PETUNIM, Yu.1.
--- --.- - Notion of the minimal scale of spaces. UAL All SSSR 154 no.l:
30-33 Ja'64. (MIRA 17:2)
1. Voronezhskiy gosudarstvennyy univeraitet. Predstavleno
akademikom I.G. Petrovskim.

ACCESSION NR: AP4025104 8/0020/64/155/003/0499/0502
AUTHORSt Askerov, N. 0.; Kreyn# S. G.; Laptevo G. 1.
TITLE: One class of not self-adjoint boundary value problems
SOURCE: AN SSSR. Doklady*, v. 155, no- 3, 1964, 499-302
TOPIC TAGS: boundary value problem, differential
equation, mathematical physical differential operator, Hilbert
space, scalar product, linear operator, Riesz theorem
ABSTRACT: A number of problems in mathematical physics can be
reduced to homogeneous boundary value problems with one and the
same parameter x in the differential equations and boundary condi-
tions* In spite of the fact that with every fixed A, the differ-
ential operator and boundary conditions are self-adjoint, the
problem is very often not self-adjoint; the spectrum can be imag-
inary. The article is a general examination of one class of these
problems. Suppose a linear operator A with an eve 'here dense
domain of definition D(A) is given in a separable 7-,Wlbert space H
with a scalar product ( ). Also ouppoze that two linear opera-
.La~s T Ind:r, mapping D(A) into some other separable Hilbert space
4
.....................

ACCESSION NR: AP4025104
H, with scalar product are defined on D(A). The operators
~Ay T andr have the following properties: totality of the elements
of DIA) satisfying the conditionsTv - 0 and n - 0, dense in H;
Ithe restriction Ao of the operator A to the set of all elements of
)D(A), for which Tv - 01 is a self-adjoint, positively defined
!operator having a completely continuols reciprocal; and the opera-
Itor 2' maps D(A ) into a set, dense in H j and is thus as completely
!continuous as the operator from the space HP/,into the space His The
!Green formula
(Au, v) - AN, v, (Tu, rv).1
;where A(u,v) is a bilinedr function such that A(upu);PO, is valid*
For each ye HI there exists a unique elementwto which satisfies the
identity
rz),
for any z-6 D(Ao~). The equation
I M XPI +Q11
vas examined generally in the Hilbert space H. Here, P is positive
i
.and Q are non-negative compl9tely continuous operators in H. It can
-2/4

ACCESSION VRI AP4025104
be immediately verified that equation (3),is equivalent to the
system of equations
P"'B (V*
P'I-BP"lg +
- r-+r go
111,11 Q111 hgo
Q"-BP"Ig + Y Q r+-r
+
All eigenvalues of equation (3) have a non-negative real part. It
the condition
41PIl Qj< 1.
is fulfilled, then all the eigenvalues are real. Starting with
some number, all eigen values of the problem Ay - Xy, %Ty - 0"I are
real. If the condition I ire 11
- 00, 1