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Published in:
2019 | OriginalPaper | Chapter
8. Review of Classical Non-self-adjoint Spectral Theory
Author : Johannes Sjöstrand
Published in: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
Publisher: Springer International Publishing
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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).