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Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations. 2019 ed..
・ISBN 978-3-030-10818-2 paper EUR 109.99
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| 著者・編者 | Sjoestrand, Johannes, |
|---|---|
| シリーズ | Pseudo-Differential Operators |
| 出版社 | (Springer Nature Switzerland AG, SZ) |
| 出版年月 | 2019 |
| ページ数 | 496 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-14509＞ |
解説
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.