Spectral Theory and its Applications
eBook - PDF

Spectral Theory and its Applications

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Spectral Theory and its Applications

About this book

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.

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Yes, you can access Spectral Theory and its Applications by Bernard Helffer in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Contents
  3. 1 Introduction
  4. 2 Unbounded operators, adjoints, and self-adjoint operators
  5. 3 Representation theorems
  6. 4 Semibounded operators and the Friedrichs extension
  7. 5 Compact operators: general properties and examples
  8. 6 Spectral theory for bounded operators
  9. 7 Applications to statistical mechanics and partial differential equations
  10. 8 Self-adjoint unbounded operators and spectral theory
  11. 9 Essentially self-adjoint operators
  12. 10 The discrete spectrum and essential spectrum
  13. 11 The max–min principle
  14. 12 Spectral questions about the Rayleigh equation
  15. 13 Non-self-adjoint operators and pseudospectra
  16. 14 Applications to non-self-adjoint one-dimensional models
  17. 15 Applications in kinetic theory: the Fokker–Planck operator
  18. 16 Problems
  19. Bibliography
  20. Index