Linear operators and their spectra
著者
書誌事項
Linear operators and their spectra
（Cambridge studies in advanced mathematics, 106）
Cambridge University Press, 2007
- : hardback
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注記
Includes bibliographical references (p. 436-445) and index
内容説明・目次
内容説明
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.
目次
- 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 Schroedinger operators.
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