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Cambridge Studies in Advanced Mathematics #106: Linear Operators and Their Spectra

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Publisher Comments:

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.

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.

Synopsis:

Authoritative text presenting a broad view of the spectral theory of non-self-adjoint linear operators.

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.

Product Details

ISBN:
9780521866293
Author:
Davies, E. Brian
Publisher:
Cambridge University Press
Location:
Cambridge
Subject:
Differential Equations
Subject:
Linear operators
Subject:
Spectral theory (Mathematics)
Subject:
Mathematics-Differential Equations
Edition Description:
Hardcover
Series:
Cambridge Studies in Advanced Mathematics
Series Volume:
106
Publication Date:
20070631
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
15 line diagrams 274 exercises 15 fi
Pages:
451
Dimensions:
9.18x6.41x1.12 in. 1.68 lbs.

Related Subjects

History and Social Science » Politics » General
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Operator Analysis

Cambridge Studies in Advanced Mathematics #106: Linear Operators and Their Spectra New Hardcover
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Product details 451 pages Cambridge University Press - English 9780521866293 Reviews:
"Synopsis" by , 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.
"Synopsis" by , Authoritative text presenting a broad view of the spectral theory of non-self-adjoint linear operators.
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