Linear Operators and their Spectra

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

E. Brian Davies is a Professor of Mathematics at King's College London and a Fellow of the Royal Society. This is his seventh book.

Zusammenfassung

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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2017
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9780521866293
ISBN-10:	0521866294
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Davies, E. Brian
Hersteller:	Cambridge University Press
Maße:	235 x 157 x 32 mm
Von/Mit:	E. Brian Davies
Erscheinungsdatum:	07.06.2017
Gewicht:	0,901 kg

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