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Spectral theory and its applications

Author: Bernard Helffer
Publisher: Cambridge, UK : Cambridge University Press, [2013]
Series: Cambridge studies in advanced mathematics, 139.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra"--
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Details

Document Type: Book
All Authors / Contributors: Bernard Helffer
ISBN: 9781107032309 110703230X
OCLC Number: 808930335
Description: v, 255 pages : illustrations ; 24 cm.
Contents: 1. Introduction --
2. Unbounded operators, adjoints, and self-adjoint operators --
3. Representation theorem --
4. Semibounded operators and the Friedrichs extension --
5. Compact operators: general properties and examples --
6. Spectral theory for bounded operators --
7. Applications to statistical mechanics and partial differential equations --
8. Self-adjoint unbounded operators and spectral theory --
9. Essentially self-adjoint operators --
10. Discrete spectrum, essential spectrum --
11. The max-min principle --
12. Special questions about the Rayleigh equation --13. Non-self adjoint operators and pseudospectra --14. Applications to non-self-adjoint one-dimensional models --
15. Applications in kinetic theory: the Fokker-Planck operator --
16. Problems.
Series Title: Cambridge studies in advanced mathematics, 139.
Responsibility: Bernard Helffer, Université Paris-Sud.

Abstract:

Introduces the basic tools in spectral analysis using numerous examples from the Schrodinger operator theory and various branches of physics.  Read more...
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"It is written in a way well suited for a graduate course." Pavel V. Exner, Mathematical Reviews

 
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