Author | Demuth, Michael. author |
---|---|
Title | Stochastic Spectral Theory for Selfadjoint Feller Operators [electronic resource] : A functional integration approach / by Michael Demuth, Jan A. van Casteren |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8460-0 |
Descript | XII, 463 p. online resource |
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 Schrรถdinger 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 Diniโs Lemma, Scheffรฉโs Theorem, Monotone Class Theorem -- References -- Index of Symbols