Operator Theory Nonclassical Problems

Operator Theory Nonclassical Problems

by S. G. Pyatkov, Sergei G. Pyatkov
     
 

ISBN-10: 9067643637

ISBN-13: 9789067643634

Pub. Date: 04/28/2002

Publisher: De Gruyter

This monograph describes mathematical methods applicable to studying nonclassical problems of mathematical physics. The emphasis of the book is on

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Overview

This monograph describes mathematical methods applicable to studying nonclassical problems of mathematical physics. The emphasis of the book is on applications of the interpolar theory of Banach spaces to the theory of linear operators to be expotentially dichotomous, to some continuity properties of linear operators in Hilbert scales, to the Riesz basis property of eigenelements and associated elements of linear pencils and the correspondending elliptic problems with indefinite weight functions, and to studying nonclassical boundary value problems for first order operator-differential equations.

Product Details

ISBN-13:
9789067643634
Publisher:
De Gruyter
Publication date:
04/28/2002
Series:
Inverse and III-Posed Problems Series, #33
Pages:
364
Product dimensions:
6.69(w) x 9.61(h) x 0.81(d)
Age Range:
18 Years

Table of Contents

Ch. 1Indefinite inner product spaces. Linear operators. Interpolation1
1Indefinite inner product spaces2
2The basic classes of operators in Krein spaces14
3Interpolation of Banach and Hilbert spaces and applications23
4The existence of maximal semidefinite invariant subspaces for J dissipative operators52
5First order equations. Decomposition of a solution77
Ch. 2Spectral theory for linear selfadjoint pencils111
1Examples112
2Basic assumptions. The structure of root subspaces114
3The Riesz basis property. Invariant subspaces127
4Sufficient conditions147
Ch. 3Elliptic eigenvalue problems with an indefinite weight function151
1Auxiliary function spaces. Interpolation153
2Preliminaries. Basic assumptions209
3Basisness theorems220
4Examples and counterexamples236
Ch. 4Operator-differential equations253
1Generalized solutions. Positive definite case255
2Degenerate case268
3The Fourier method291
4Some applications to partial differential equations302
Bibliography323
Index347

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