Synopses & Reviews
Authoritative text presenting a broad view of the spectral theory of non-self-adjoint linear operators.
Synopsis
This wide ranging account of the spectral theory of non-self-adjoint linear operators discusses topics such as Fredholm theory, Hilbert-Schmidt and trace class operators, 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, presenting recent analysis by the author and Barry Simon. With many illustrative examples and exercises, this authoritative text presents a broad view of the topic of linear operators and their spectra.
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.