Titlebook: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations; Johannes Sj?strand Book 2019 Springer Nature Switz

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Introduction,others.) Abstract theory with the machinery of s-numbers can be found in the book of Gohberg and Krein. Other quite classical results concern upper bounds on the number of eigenvalues in various regions of the complex plane and questions about completeness of the set of all generalized eigenvectors.

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Spectrum and Pseudo-Spectrum78), Riesz and Sz.-Nagy (Le?ons d’analyse fonctionnelle, Quatrième édition. Académie des Sciences de Hongrie, Gauthier-Villars, Editeur- Imprimeur-Libraire, Paris; Akadémiai Kiadó, Budapest 1965) for more substantial presentations.

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The Complex WKB MethodIn this chapter we shall study the exponential growth and asymptotic expansions of exact solutions of second-order differential equations in the semi-classical limit. As an application, we establish a Bohr-Sommerfeld quantization condition for Schr?dinger operators with real-analytic complex-valued potentials.

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Weyl Asymptotics for the Damped Wave EquationThe damped wave equation is closely related to non-self-adjoint perturbations of a self-adjoint operator . of the form . Here, . is a semi-classical pseudodifferential operator of order 0 on ..(.), where we consider two cases:

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Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations978-3-030-10819-9Series ISSN 2297-0355 Series E-ISSN 2297-0363