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Review of Classical Non-self-adjoint Spectral Theory

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

Abstract

The first section of this chapter deals with Fredholm theory in the spirit of Appendix A in Helffer and Sjöstrand (Mm Soc Math Fr (NS) 24–25:1–228, 1986), 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 (Lectures on Resonances) which is a brief account of parts of the classical book by Gohberg and Krein (Introduction to the Theory of Linear Non-Selfadjoint Operators. Translations of Mathematical Monographs, vol 18. AMS, Providence, 1969).

References

  1. 4.
    L. Ahlfors, Complex analysis. An Introduction to the Theory of Analytic Functions of One Complex Variable, 3rd edn. International Series in Pure and Applied Mathematics (McGraw-Hill Book Co., New York, 1978)Google Scholar
  2. 48.
    I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Non-selfadjoint Operators. Translations of Mathematical Monographs, vol. 18 (AMS, Providence, 1969)Google Scholar
  3. 60.
    B. Helffer, J. Sjöstrand, Résonances en limite semi-classique. Mém. Soc. Math. France (N.S.), vol. 24–25 (Gauthier-Villars, Paris, 1986), pp. 1–228CrossRefGoogle Scholar
  4. 105.
    A. Melin, J. Sjöstrand, Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2. Astérique 284, 181–244 (2003). https://arxiv.org/abs/math/0111293 MathSciNetzbMATHGoogle Scholar
  5. 136.
    J. Sjöstrand, Lectures on Resonances (2007). http://sjostrand.perso.math.cnrs.fr/Coursgbg.pdf
  6. 144.
    J. Sjöstrand, Weyl Law for Semi-classical Resonances with Randomly Perturbed Potentials. Mém. de la SMF 136, 144 (2014). http://arxiv.org/abs/1111.3549 MathSciNetzbMATHGoogle Scholar
  7. 148.
    J. Sjöstrand, M. Zworski, Elementary linear algebra for advanced spectral problems. Ann. Inst. Fourier 57(7), 2095–2141 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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