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Spectral theory and applications /

This book is a collection of lecture notes and survey papers based on the minicourses given by leading experts at the 2016 CRM Summer School on Spectral Theory and Applications, held from July 4-14, 2016, at Université Laval, Québec City, Québec, Canada. The papers contained in the volume cover a...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Girouard, Alexandre, 1976- (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : Montreal, Quebec, Canada : American Mathematical Society ; Centre de Recherches Mathematiques, [2018]
Colección:Contemporary mathematics (American Mathematical Society). Centre de recherches mathématiques proceedings ; v. 720.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Title page; Contents; Preface; Fundamentals of spectral theory; Introduction; 1. Normed spaces and operators; 2. Invertible operators; 3. The spectrum; 4. Hilbert spaces; 5. Operators on Hilbert spaces; 6. Compact operators; 7. The spectral theorem; 8. Sturm-Liouville equation; Spectral theory of partial differential equations; 1. Resources, prerequisites and notation; 2. Computable spectra and qualitative properties-Laplacian; 3. Discrete spectral theorem for sesquilinear forms; 4. Variational characterizations of eigenvalues; 5. Application: Discrete spectrum for the Laplacian
  • 6. Application: Monotonicity properties of eigenvalues7. Case study: Stability of steady states for reaction-diffusion PDEs; Appendix A. Compact imbeddings of Sobolev space into ²; References; From classical mechanics to quantum mechanics; 1. Classical mechanics; 2. Review of probability and operator theory; 3. Quantum mechanics; 4. Hidden variables and non-locality; References; Numerical methods for spectral theory; 1. Introduction; 2. Finite difference methods; 3. Finite element methods; 4. Solution of matrix eigenvalue problems; 5. Application: Vibrating plates; 6. Further reading
  • Acknowledgments7. Exercises; References; Spectral geometry; 1. What makes the Laplacian special?; 2. The Laplacian on a Riemannian manifold; 3. Hearing the geometry of a manifold; 4. Exercises; Quantum graphs via exercises; 1. Basic spectral theory of quantum graphs; 2. Trace formula and periodic orbits; 3. Further topics; Acknowledgments; References; Spectral properties of classical integral operators and geometry; 1. Classical integral operators; 2. Single-layer potentials; 3. Double-layer potentials; Acknowledgments; References; Back Cover