Linear Operators and Their Spectra
By (author) E. Brian Davies
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Linear Operators and Their Spectra by E. Brian Davies
Book DescriptionThis 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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Book DetailsISBN: 9780521866293
(228mm x 152mm x 27mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 26-Apr-2007
Country of Publication: United Kingdom
Books By Author E. Brian Davies
Why Beliefs Matter, Paperback (April 2014)
This book discusses deep problems about our place in the world with a minimum of jargon. It argues that 'absolutist' ideas dating back to Plato continue to mislead generations of mathematicians, physicists, and theologians, and reveals the underlying reasons for the current conflicts between science and religion.
Science in the Looking Glass, Paperback (June 2007)
How do scientific conjectures become laws? Why do some laws turn out to be wrong? Why does proof mean different things in different sciences? Experience shows that disentangling scientific knowledge from opinion is harder than one might expect. Full of illuminating examples and quotations, this book brings alive issues at the heart of all science.
Spectral Theory and Geometry, Paperback (September 1999)» View all books by E. Brian Davies
Authoritative lectures from world experts on spectral theory and geometry.
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Author Biography - E. Brian Davies
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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