Title: Linear Operators and their Spectra (Cambridge Studies in Advanced Mathematics, Series Number 106)
Publisher: Cambridge University Press
Publication Date: 2007
Language: English
ISBN 10: 0521866294
ISBN 13: 9780521866293
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

About the Author

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.

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