Linear Operators and their Spectra

Linear Operators and their Spectra

by E. Brian Davies
     
 

ISBN-10: 0521866294

ISBN-13: 9780521866293

Pub. Date: 04/30/2007

Publisher: Cambridge University Press

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

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Overview

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.

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Product Details

ISBN-13:
9780521866293
Publisher:
Cambridge University Press
Publication date:
04/30/2007
Series:
Cambridge Studies in Advanced Mathematics Series, #106
Pages:
464
Product dimensions:
5.98(w) x 8.98(h) x 1.06(d)

Table of Contents

Preface; 1. Elementary operator theory; 2. Function spaces; 3. Fourier transforms and bases; 4. Intermediate operator theory; 5. Operators on Hilbert space; 6. One-parameter semigroups; 7. Special classes of semigroup; 8. Resolvents and generators; 9. Quantitative bounds on operators; 10. Quantitative bounds on semigroups; 11. Perturbation theory; 12. Markov chains and graphs; 13. Positive semigroups; 14. NSA Schrödinger operators.

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