Spectral Theory and its Applications (Cambridge Studies in Advanced Mathematics, Series Number 139)

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. 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-- 1. Introduction -- 2. Unbounded Operators, Adjoints, And Self-adjoint Operators -- 3. Representation Theorems -- 4. Semibounded Operators And The Friedrichs Extension -- 5. Compact Operators: General Properties And Examples -- 6. Spectral Theory For Bounded Operators -- 7. Applications To Statistical Mechanics And Partial Differential Equations -- 8. Self-adjoint Unbounded Operators And Spectral Theory -- 9. Essentially Self-adjoint Operators -- 10. Discrete Spectrum And Essential Spectrum -- 11. The Max-min Principle -- 12. Spectral Questions About The Rayleigh Equation -- 13. Non-self-adjoint Operators And Pseudospectra -- 14. Applications To Non-self-adjoint One-dimensional Models -- 15. Applications In Kinetic Theory: The Fokker-planck Operator -- 16. Problems. Bernard Helffer. Includes Bibliographical References (pages 248-252) And Index. "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"-- Provided by publisher Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics