Spectral Theory and Its Applications

ISBN-13: 9781107032309 / Angielski / Twarda / 2013 / 262 str.

Bernard Helffer

Opis

Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrodinger 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."

Recenzje

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

Spis treści

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.