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Titlebook: Stochastic Spectral Theory for Selfadjoint Feller Operators; A Functional Integra Michael Demuth,Jan A. Casteren Book 2000 Birkhäuser Verla

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书目名称Stochastic Spectral Theory for Selfadjoint Feller Operators
副标题A Functional Integra
编辑Michael Demuth,Jan A. Casteren
视频videohttp://file.papertrans.cn/879/878163/878163.mp4
丛书名称Probability and Its Applications
图书封面Titlebook: Stochastic Spectral Theory for Selfadjoint Feller Operators; A Functional Integra Michael Demuth,Jan A. Casteren Book 2000 Birkhäuser Verla
描述.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..
出版日期Book 2000
关键词Feynman-Kac formula; Markov; Markov process; Martingale; Ornstein-Uhlenbeck process; Probability theory; m
版次1
doihttps://doi.org/10.1007/978-3-0348-8460-0
isbn_softcover978-3-0348-9577-4
isbn_ebook978-3-0348-8460-0Series ISSN 2297-0371 Series E-ISSN 2297-0398
issn_series 2297-0371
copyrightBirkhäuser Verlag 2000
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Convergence of Resolvent Differences,d region in.as discussed in the beginning of section C of Chapter 2. This means that we introduce a new self-adjoint operator.given by..in .(., .) with dom (.) = dom (.)We also introduced the operator . in Definition 2.25 as the generator of the Dirichlet semigroup onL.(∑, .):
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Perturbations of Free Feller Operators,r-product formula to find a Feynman-Kac representation of the perturbed semigroup. The semi-analytic or semi-stochastic manner begins again with the unperturbed semi-group. Then the potentials are introduced stochastically by verifying the sensibility and the semigroup property of the Feynman-Kac fo
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Hilbert-Schmidt Properties of Resolvent and Semigroup Differences,dly, there will be a potential barrier on F, a closed subset of.The aim of this chapter is to study Hilbert-Schmidt properties for resolvent and/or semigroup differences corresponding to both kinds of perturbations. In part A we consider regular perturbations. The main results and estimates in secti
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Convergence of Resolvent Differences,e Feller operator as introduced in Definition 2.8 (see Theorem 2.5.(a) as well). Here K.is the free Feller operator (see Definition 1.3) and V is a Kato-Feller potential given in Definition 2.1. The operator . is perturbed by a potential of the form ß1ГHere ß is a positive parameter and Г is a close
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