Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
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 …
Read More ↓Title Statements
- Full title :Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations / by Johannes Sjöstrand.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2019.
- Edition:1st ed. 2019
Publication Statements
- Publisher(s):Imprint: Birkhäuser, Springer International Publishing
- Place of Publication:Cham
- Language:eng
- Publication Date:2019.
The Physical Object
- Description:X, 496 p. 71 illus., 69 illus. in color. :
Edition Identifiers
- ISBN:9783030108199, 3030108198
- oclc:on1204021846
- LC Classification:QA331-355
- Dewey Decimal:515.9
Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Equations différentielles p-adiques: applications aux sommes exponentielles
Christol, Gilles
Transformations of manifolds and applications to differential equations
Tenenblat, Keti
Computational methods in engineering and science: with applications to fluid dynamics and…
Nakamura, Shoichiro
Computational methods in engineering and science: with applications to fluid dynamics and…
Nakamura, Shoichiro
Rate & Review