Overview

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.

Full Product Details

Author:   Michael Demuth ,  Jan A. van Casteren
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   Softcover reprint of the original 1st ed. 2000
Dimensions:   Width: 15.50cm , Height: 2.40cm , Length: 23.50cm
Weight:   0.730kg
ISBN:  

9783034895774

ISBN 10:   3034895771
Pages:   463
Publication Date:   23 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions