Overview
- Presents new results of a classic field
- Includes open problems
- Describes recent developments on topics in non-self-adjoint operator theory
Part of the book series: Pseudo-Differential Operators (PDO, volume 14)
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Table of contents (20 chapters)
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Front Matter
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Basic Notions, Differential Operators in One Dimension
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Front Matter
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Spectral Asymptotics for Differential Operators in Higher Dimension
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Front Matter
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Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
Authors: Johannes Sjöstrand
Series Title: Pseudo-Differential Operators
DOI: https://doi.org/10.1007/978-3-030-10819-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-10818-2Published: 29 May 2019
eBook ISBN: 978-3-030-10819-9Published: 17 May 2019
Series ISSN: 2297-0355
Series E-ISSN: 2297-0363
Edition Number: 1
Number of Pages: X, 496
Number of Illustrations: 2 b/w illustrations, 69 illustrations in colour
Topics: Functions of a Complex Variable, Several Complex Variables and Analytic Spaces, Ordinary Differential Equations, Partial Differential Equations, Operator Theory