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Spectral theory and its applications / Bernard Helffer.

By: Material type: TextTextSeries: Cambridge studies in advanced mathematics ; 139Publication details: Cambridge : Cambridge University Press, 2013.Description: v, 255 p. : illustrations ; 24 cmISBN:
  • 9781107032309 (hardback)
Subject(s): DDC classification:
  • 515.7222 23 H474
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-- Bibliography-- Index.
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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.7222 H474 (Browse shelf(Opens below)) Available 135738
Total holds: 0

Includes bibliographical references (pages 248-252) and index.

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--
Bibliography--
Index.

"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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