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2019 | OriginalPaper | Chapter

2. Spectrum and Pseudo-Spectrum

Author : Johannes Sjöstrand

Published in: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations

Publisher: Springer International Publishing

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Abstract

In this book all Hilbert spaces will be assumed to separable for simplicity. In this section we review some basic definitions and properties; we refer 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. Fourier analysis, self adjointness. Academic, New York, 1975; Methods of modern mathematical physics. IV. Analysis of operators. Academic, New York, 1978), Riesz and Sz.-Nagy (Leçons 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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previous chapter Introduction
next chapter Weyl Asymptotics and Random Perturbations in a One-Dimensional Semi-classical Case
Footnotes
1
Linear in the first argument and anti-linear in the second.
 
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Metadata
Title
Spectrum and Pseudo-Spectrum
Author
Johannes Sjöstrand
Copyright Year
2019
Book
Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations

Print ISBN: 978-3-030-10818-2

Electronic ISBN: 978-3-030-10819-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-10819-9_2

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