Stochastic spectral theory for selfadjoint Feller operators : a functional integration approach

This text assumes no knowledge of mathematical logic. Beginning with a nonstandard construction of the real number system, it leads students thorough the basic topics of elementary real analysis, topological spaces, and Hilbert space. Includes nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. 1977 edition "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 scattered 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."--BOOK JACKET. 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