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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated.
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.
Authors and Affiliations
Bibliographic Information
Book Title: Stochastic Spectral Theory for Selfadjoint Feller Operators
Book Subtitle: A Functional Integration Approach
Authors: Michael Demuth, Jan A. Casteren
Series Title: Probability and Its Applications
DOI: https://doi.org/10.1007/978-3-0348-8460-0
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Birkhäuser Verlag 2000
Hardcover ISBN: 978-3-7643-5887-7Published: 27 July 2000
Softcover ISBN: 978-3-0348-9577-4Published: 23 October 2012
eBook ISBN: 978-3-0348-8460-0Published: 06 December 2012
Series ISSN: 2297-0371
Series E-ISSN: 2297-0398
Edition Number: 1
Number of Pages: XII, 463
Topics: Mathematical and Computational Engineering, Applications of Mathematics, Probability Theory and Stochastic Processes, Operator Theory