Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
Authors: Sjöstrand, Johannes
Free Preview- Presents new results of a classic field
- Includes open problems
- Describes recent developments on topics in non-self-adjoint operator theory
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- About this book
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The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago.
In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book.
Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
- Table of contents (20 chapters)
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Introduction
Pages 1-5
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Spectrum and Pseudo-Spectrum
Pages 9-28
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Weyl Asymptotics and Random Perturbations in a One-Dimensional Semi-classical Case
Pages 29-52
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Quasi-Modes and Spectral Instability in One Dimension
Pages 53-65
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Spectral Asymptotics for More General Operators in One Dimension
Pages 67-91
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Table of contents (20 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
- Authors
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- Johannes Sjöstrand
- Series Title
- Pseudo-Differential Operators
- Series Volume
- 14
- Copyright
- 2019
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-10819-9
- DOI
- 10.1007/978-3-030-10819-9
- Softcover ISBN
- 978-3-030-10818-2
- Series ISSN
- 2297-0355
- Edition Number
- 1
- Number of Pages
- X, 496
- Number of Illustrations
- 2 b/w illustrations, 69 illustrations in colour
- Topics