Pseudo-Differential Operators

Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations

Authors: Sjöstrand, Johannes

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  • 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

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)

Table of contents (20 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-10819-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-3-030-10818-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
Authors
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