Review of Classical Non-self-adjoint Spectral Theory

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


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).


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Authors and Affiliations

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

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