Spectral Theory and its Applications

Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

Bernard Helffer (Author)

9781107032309, Cambridge University Press

Hardback, published 17 January 2013

262 pages, 2 b/w illus. 80 exercises
23.1 x 15.2 x 1.8 cm, 0.45 kg

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

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.

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.

Subject Areas: Mathematical physics [PHU], Fluid mechanics [PHDF], Integral calculus & equations [PBKL], Differential calculus & equations [PBKJ]