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Stochastic Spectral Theory for Selfadjoint Feller Operators

A functional integration approach

  • Michael Demuth
  • Jan A. van Casteren

Part of the Probability and Its Applications book series (PA)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Michael Demuth, Jan A. van Casteren
    Pages 1-52
  3. Michael Demuth, Jan A. van Casteren
    Pages 53-102
  4. Michael Demuth, Jan A. van Casteren
    Pages 103-128
  5. Michael Demuth, Jan A. van Casteren
    Pages 129-160
  6. Michael Demuth, Jan A. van Casteren
    Pages 161-204
  7. Michael Demuth, Jan A. van Casteren
    Pages 205-232
  8. Michael Demuth, Jan A. van Casteren
    Pages 233-256
  9. Michael Demuth, Jan A. van Casteren
    Pages 257-332
  10. Back Matter
    Pages 333-463

About this book

Introduction

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.

Keywords

Feynman-Kac formula Markov Markov process Martingale Ornstein-Uhlenbeck process Probability theory mathematical physics operator operator theory scattering theory

Authors and affiliations

  • Michael Demuth
    • 1
  • Jan A. van Casteren
    • 2
  1. 1.Institut für MathematikTechnische Universität ClausthalClausthal-ZellerfeldGermany
  2. 2.Department of Mathematics and Computer ScienceUniversity of Antwerp (UIA)AntwerpBelgium

Bibliographic information

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