Linear Operators and Their Spectra

Davies, E. Brian

ISBN 10: 0521866294 / ISBN 13: 9780521866293

Published by West Nyack, New York, U.S.A.: Cambridge Univ Pr, 2007

About this Item

Hardcover in very good condition. Seller Inventory # 142619

Bibliographic Details

Title: Linear Operators and Their Spectra

Publisher: West Nyack, New York, U.S.A.: Cambridge Univ Pr

Publication Date: 2007

Binding: Hardcover

Condition: Very Good

Edition: 1st Edition

About this title

Synopsis:

This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.

Book Description:

This authoritative text presents a broad view of the spectral theory of non-self-adjoint linear operators and contains many illustrative examples and exercises. Topics discussed include Fredholm theory, Hilbert-Schmidt and trace class operators, one-parameter semigroups, perturbations of their generators and a thorough account of the new theory of pseudospectra.