Abstract
The objective of stochastic spectral analysis is explained. It is used to study regular perturbations for a general class of generators of Feller semigroups, also called generalized Schrödinger operators. Upon introducing the Kato-Feller norm, the asymptotic behaviour of several spectral data can be studied. In the present article mainly the convergence of scattering matrices is considered.
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References
J.A. van Casteren, Generators of strongly continuous semigroups, Research Notes in Mathematics 115, Pitman, London 1985.
J.A. van Casteren, A pointwise inequality for generalized Schrödinger semi-groups, in Symposium “Partial differential equations” Holzhau 1988, Teubner Texte zur Mathematik 112, 298–312, Leipzig (1989).
R. Carmona, W.C. Masters and B. Simon, Relativistic Schrödinger operators, J. Funct. Analysis 51, 117–142, (1990).
E.B. Davies, Heat kernel bounds, conservation of probability and the Feller property, Preprint King’s College London, 1991.
M. Demuth, On topics in spectral and stochastic analysis for Schrödinger operators, in “Recent Developments in Quantum Mechanics”, 223–234, Kluwer, Dordrecht (1990).
M. Demuth and J.A. van Casteren, On spectral theory for selfadjoint Feller generators, Reviews in Math. Physics 1, 325–414 (1989).
M. Demuth and J.A. van Casteren, On spectral theory for selfadjoint Feller generators II, Preprint University of Antwerp (UTA), to be published 1992.
N. Jacob, A class of elliptic differential operators generating symmetric Dirichlet forms, Preprint University of Erlangen-Nürnberg, 1990.
A.N. Kochubeí, Singular parabolic equations, hypersingular integrals and Markov processes, Math. Izvestiya USSR, 33, 233–259 (1989).
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© 1992 Springer-Verlag Berlin Heidelberg
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Demuth, M., van Casteren, J.A. (1992). Perturbations of Generalized Schrödinger Operators in Stochastic Spectral Analysis. In: Balslev, E. (eds) Schrödinger Operators The Quantum Mechanical Many-Body Problem. Lecture Notes in Physics, vol 403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55490-4_1
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DOI: https://doi.org/10.1007/3-540-55490-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-13888-5
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