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

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Spectrum and Pseudo-Spectrum to Kato (Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer, New York, 1966), Reed and Simon (Methods of modern mathematical physics. I. Functional analysis, 2nd edn. Academic, New York, 1980; Methods of modern mathematical physics. II. F

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Resolvent Estimates Near the Boundary of the Range of the Symboldary-like” points.) The result is due (up to a small generalization) to Montrieux (Estimation de résolvante et construction de quasimode pres du bord du pseudospectre, 2013) and improves earlier results by Martinet (Sur les propriétés spectrales d’opérateurs nonautoadjoints provenant de la mécanique

cancellous-bone

Review of Classical Non-self-adjoint Spectral Theory86), see also an appendix in Melin and Sjöstrand (Astérique 284:181–244, 2003) and Sjöstrand and Zworski (Ann Inst Fourier 57:2095–2141, 2007). The remaining sections give a brief account of the very beautiful classical theory of non-self-adjoint operators, taken from a section in Sjöstrand (Lecture

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Obedient

From Resolvent Estimates to Semigroup Bounds chapter we discuss some abstract results of that type, including the Hille–Yoshida and Gearhardt–Prüss–Hwang–Greiner theorems. As for the latter, we also give a result of Helffer and the author that provides a more precise bound on the semigroup.