Operator theory

Operator theory: nonclassical problems

by Pyatkov, S. G.

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Title Statements

  • Full title :Operator theory : nonclassical problems / S.G. Pyatkov.

Edition Statements

  • Publication Date:2002.

Publication Statements

  • Publisher(s):VSP
  • Place of Publication:Utrecht
  • Language:eng
  • Publication Date:2002.

The Physical Object

  • Description:1 online resource (ix, 346 pages)

Edition Identifiers

  • ISBN:9783110900163, 3110900165
  • oclc:ocn859155009
  • LC Classification:QA329
  • Dewey Decimal:515/.724

Table of Contents

Chapter 1. Indefinite inner product spaces. Linear operators. Interpolation -- 1. Indefinite inner product spaces -- 1.1. Definitions -- 1.2. Krein spaces -- 1.3. The Gram operator. W-spaces -- 1.4. J-orthogonal complements. Projective completeness -- 1.5. J-orthonormalized systems -- 2. The basic classes of operators in Krein spaces -- 2.1. J-dissipative operators -- 2.2. J-selfadjoint operators -- 3. Interpolation of Banach and Hilbert spaces and applications -- 3.1. Preliminaries -- 3.2. Continuity of some functional in a Hilbert scale

3.3. Separation of the spectrum of an unbounded operator3.4. Interpolation properties of bases -- 4. The existence of maximal semidefinite invariant subspaces for J-dissipative operators -- 5. First order equations. Decomposition of a solution -- 5.1. Function spaces -- 5.2. The Cauchy problem -- 5.3. Auxiliary definitions. Some properties of imaginary powers of operators -- 5.4. Solvability of the Cauchy problem in the original Banach space -- 5.5. Adjoint problems -- 5.6. Arbitrary operators. Phase spaces -- 5.7. Remarks and examples

Chapter 2. Spectral theory for linear selfadjoint pencils1. Examples -- 1.1. Selfadjoint pencils -- 1.2. Ellip…

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Subjects

Banach spaces Espaces d'interpolation Espaces de Banach Interpolation spaces Logique mathématique non classique MATHEMATICS -- Calculus Mathematics -- Mathematical Analysis Nonclassical mathematical logic Operator theory Théorie des opérateurs

Writers

Pyatkov, S. G.

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