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Stochastic Spectral Theory for Selfadjoint Feller Operators

  • Livre Relié
  • 463 Nombre de pages
A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral t... Lire la suite
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Description

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.

Contenu

Basic assumptions of stochastic spectral analysis -free Feller operators; perturbations of free Feller operators; proof of continuity and symmetry of Feynman-Kac kernels; resolvent and semigroup differences for Feller operators - operator norms; Hilbert-Schmidt properties of resolvent and semigroup differences; trace class properties of semigroup differences; convergence of resolvent differences; spectral properties of self-adjoin Feller operators. appendices: spectral theory; semigroup theory; Markov processes, Martingales and stopping times; Dirichlet kernels, harmonic measures, capacities; Dini's lemma; scheffe's theorem, monotone class theorem.

Détails sur le produit

Titre: Stochastic Spectral Theory for Selfadjoint Feller Operators
Auteur:
Code EAN: 9783764358877
ISBN: 978-3-7643-5887-7
Format: Livre Relié
Genre: Technique
nombre de pages: 463
Poids: 848g
Taille: H235mm x B235mm
Année: 2000
Auflage: 2000