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Linear Operators and their Spectra book cover
Linear Operators and their Spectra
2007
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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.
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Author

E Brian Davies
E Brian Davies
Author · 4 books

E. Brian Davies was awarded a first class degree in Mathematics at the University of Oxford in 1965 and a D Phil., also at Oxford, in 1968, when he was also awarded the Senior Mathematical Prize. After two years in the USA, at Princeton and MIT, he took up a permanent position as a Tutorial Fellow at St John’s College, Oxford. From 1973 he was a University Lecturer at the University of Oxford. In 1981 Davies was appointed as Professor of Mathematics at King's College, London, where he remained until his official retirement in 2010. He was Head of Department between 1990 and 1993. He was the founding Editor of the London Mathematical Society Student Texts between 1983 and 1990, and the founding Editor of the Journal of Spectral Theory, published by the European Mathematical Society, from 2010. In March 1995 Davies was elected a Fellow of the Royal Society, in recognition of his seminal work in spectral theory and particularly on the heat kernels of diffusion equations, of great relevance in quantum theory and other fields. In June 1996 he was elected a Fellow of King's College, London. In June 1998 he was awarded the Senior Berwick Prize by the London Mathematical Society. He was President of the London Mathematical Society in 2008 and 2009. As well as over two hundred research papers, Davies has published five monographs and two popular books on the philosophy of mathematics and science.

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