Stochastic Spectral Theory for Selfadjoint Feller Operators: A Functional Integration Approach: Probability and Its Applications
Autor Michael Demuth, Jan A. van Casterenen Limba Engleză Paperback – 23 oct 2012
A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattering systems.
The unified approach provides a new viewpoint of and a deeper insight into the subject. The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.
Toate formatele și edițiile | Preț | Express |
---|---|---|
Paperback (1) | 649.39 lei 43-57 zile | |
Birkhäuser Basel – 23 oct 2012 | 649.39 lei 43-57 zile | |
Hardback (1) | 655.78 lei 43-57 zile | |
Birkhäuser Basel – 27 iul 2000 | 655.78 lei 43-57 zile |
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Specificații
ISBN-13: 9783034895774
ISBN-10: 3034895771
Pagini: 480
Ilustrații: XII, 463 p.
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.67 kg
Ediția:Softcover reprint of the original 1st ed. 2000
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Probability and Its Applications
Locul publicării:Basel, Switzerland
ISBN-10: 3034895771
Pagini: 480
Ilustrații: XII, 463 p.
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.67 kg
Ediția:Softcover reprint of the original 1st ed. 2000
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Probability and Its Applications
Locul publicării:Basel, Switzerland
Public țintă
ResearchCuprins
1 Basic Assumptions of Stochastic Spectral Analysis:Free Feller Operators.- A Introduction.- B Assumptions and Free Feller Generators.- C Examples.- D Heat kernels.- E Summary of Schrödinger semigroup theory.- 2 Perturbations of Free Feller Operators.- The framework of stochastic spectral analysis.- A Regular perturbations.- B Integral kernels, martingales, pinned measures.- C Singular perturbations.- 3 Proof of Continuity and Symmetry of Feynman-Kac Kernels.- 4 Resolvent and Semigroup Differences for Feller Operators: Operator Norms.- A Regular perturbations.- B Singular perturbations.- 5 Hilbert-Schmidt Properties of Resolvent and Semigroup Differences.- A Regular perturbations.- B Singular perturbations.- 6 Trace Class Properties of Semigroup Differences.- A General trace class criteria.- B Regular perturbations.- C Singular perturbations.- 7 Convergence of Resolvent Differences.- 8 Spectral Properties of Self-adjoint Feller Operators.- A Qualitative spectral results.- B Quantitative estimates for regular potentials.- C Quantitative estimates for singular potentials in terms of the weighted Laplace transform of the occupation time (for large coupling parameters).- Appendix A Spectral Theory.- Appendix B Semigroup Theory.- Appendix C Markov Processes, Martingales and Stopping Times.- Appendix D Dirichlet Kernels, Harmonic Measures, Capacities.- Appendix E Dini’s Lemma, Scheffé’s Theorem, Monotone Class Theorem.- References.- Index of Symbols.