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Spectrum and Pseudo-Spectrum

  • Johannes Sjöstrand
Chapter
Part of the Pseudo-Differential Operators book series (PDO, volume 14)

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Johannes Sjöstrand
    • 1
  1. 1.Université de Bourgogne Franche-ComtéDijonFrance

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