Spectral Theory and its Applications [Hardcover]

Introduces the basic tools in spectral analysis using numerous examples from the Schr?dinger operator theory and various branches of physics.Bernard Helffer's introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schr?dinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The author's focus on applications enables readers to connect theory with practice.Bernard Helffer's introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schr?dinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The author's focus on applications enables readers to connect theory with practice.Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schr?dinger 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. l&