Stochastic Spectral Theory for Selfadjoint Feller Operators

A Functional Integration Approach

By: Michael Demuth, Jan A. van Casteren

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Hardcover | 27 July 2000

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480 Pages

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23.39 x 15.6 x 2.69

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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.

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Calculus & Mathematical Analysis Functional Analysis & Transforms Medicine Medicine in General Probability & Statistics Engineering & Technology Technology in General Maths for Engineers

Science Science in General Maths for Scientists Engineering in General

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Published: 23rd October 2012

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Preface
Basic Assumptions of Stochastic Spectral Analysis: Free Feller Operators	p. 1
Perturbations of Free Feller Operators	p. 53
Proof of Continuity and Symmetry of Feynman-Kac Kernels	p. 103
Resolvent and Semigroup Differences for Feller Operators: Operator Norms	p. 129
Hilbert-Schmidt Properties of Resolvent and Semigroup Differences	p. 161
Trace Class Properties of Semigroup Differences	p. 205
Convergence of Resolvent Differences	p. 233
Spectral Properties of Self-adjoint Feller Operators	p. 257
Spectral Theory	p. 333
Semigroup Theory	p. 345
Markov Processes, Martingales and Stopping Times	p. 353
Dirichlet Kernels, Harmonic Measures, Capacities	p. 373
Dini's Lemma, Scheffe's Theorem, Monotone Class Theorem	p. 423
References	p. 427
Index of Symbols	p. 441
Subject Index	p. 451
Table of Contents provided by Blackwell. All Rights Reserved.

Stochastic Spectral Theory for Selfadjoint Feller Operators

A Functional Integration Approach

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Hardcover

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