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Spectral Theory and its Applications

$75.99 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: February 2013
  • availability: Available
  • format: Hardback
  • isbn: 9781107032309

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About the Authors
  • 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. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.

    • Balances theory and application to bring the subject to life
    • Problems and exercises are included to help students master new material
    • A helpful introduction to current research for graduates entering the field
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    Reviews & endorsements

    "It is written in a way well suited for a graduate course."
    Pavel V. Exner, Mathematical Reviews

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    Product details

    • Date Published: February 2013
    • format: Hardback
    • isbn: 9781107032309
    • length: 262 pages
    • dimensions: 231 x 152 x 18 mm
    • weight: 0.45kg
    • contains: 2 b/w illus. 80 exercises
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Unbounded operators
    3. Representation theorems
    4. Semibounded operators
    5. Compact operators
    6. Spectral theory for bounded operators
    7. Applications in physics and PDE
    8. Spectrum for self-adjoint operators
    9. Essentially self-adjoint operators
    10. Discrete spectrum, essential spectrum
    11. The max-min principle
    12. An application to fluid mechanics
    13. Pseudospectra
    14. Applications for 1D-models
    15. Applications in kinetic theory
    16. Problems
    References
    Index.

  • Author

    Bernard Helffer, Université de Paris-Sud
    Bernard Helffer is a Professor in the Department of Mathematics at Université Paris-Sud. He has published more than 200 papers in mathematics and mathematical physics and authored five books. In 2011 he was awarded the Prix de l'État by the French Academy of Sciences.

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