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＜E-Book＞
Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations / by Johannes Sjöstrand
(Pseudo-Differential Operators, Theory and Applications. ISSN:22970363 ; 14)

Edition	1st ed. 2019.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2019
Language	English
Size	X, 496 p. 71 illus., 69 illus. in color : online resource
Authors	*Sjöstrand, Johannes author SpringerLink (Online service)
Subjects	LCSH:Functions of complex variables LCSH:Differential equations LCSH:Operator theory FREE:Functions of a Complex Variable FREE:Several Complex Variables and Analytic Spaces FREE:Differential Equations FREE:Operator Theory
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-030-10819-9

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