Non-self-adjoint differential operators, spectral asymptotics and random perturbations
- 作者： Sjostrand, Johannes, author.
- 其他作者：
- 其他題名：
- Pseudo-differential operators, theory and applications ;
- 出版： Cham : Springer International Publishing :Imprint: Birkhauser
- 叢書名： Pseudo-differential operators, theory and applications,volume 14
- 主題： Nonselfadjoint operators. , Spectral theory (Mathematics) , Functions of a Complex Variable. , Several Complex Variables and Analytic Spaces. , Ordinary Differential Equations. , Partial Differential Equations. , Operator Theory.
- ISBN： 9783030108199 (electronic bk.) 、 9783030108182 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 摘要註: 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.
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讀者標籤：
- 系統號： 005455767 | 機讀編目格式
館藏資訊
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.