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Framework and Results of Stochastic Spectral Analysis

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Mathematical Results in Quantum Mechanics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 70))

Abstract

The framework of stochastic spectral analysis is explained. The central and initial magnitude is the transition density function in a Hausdorff space. Free and perturbed Feller operators are introduced. Spectral theoretical results can be obtained by compactness, continuity in Kato-Feller norms, semi-classical and large coupling estimates. A collection of results illustrates each possibility.

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References

  1. Demuth M.; van Casteren J. (1989), On spectral theory for selfadjoint Feller generators, Rev. Math. Phys. 1, 325–414.

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  2. Demuth M. (1992), Perturbations of spectral measures for Feller operators, Operator theory: Advances and Applications, Vol. 57, 27–37.

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  3. Demuth, M.; van Casteren, J. (1992), A Hilbert-Schmidt property of resolvent differences of singularly perturbed generalized Schrödinger operators, Preprint Max-Planck-Institut Bonn, Nr. 92-48.

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  4. Demuth, M.; van Casteren, J. (1992), Perturbation of generalized Schrödinger operators in stochastic spectral analysis, Lect. Notes in Physics 403, 1-15.

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  5. Demuth, M.; Jeske, F.; Kirsch, W. (1992), On the rate of convergence for large coupling limits in quantum mechanics, Preprint Max — Planck — Institut Bonn, Nr.92 — 29. To be published in Ann. Inst. H. Poincaré.

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  6. Demuth, M.; Kirsch, W.; Mc Gillivray, J.(1993), Schrödinger semigroups — geometric estimates in terms of the occupation time. To be published in the Preprint series of the Max-Planck-Institute, Bonn.

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  7. Stollmann, P. (1992), Scattering by obstacles, Preprint Univ. of Frankfurt/Main, to be published in J. Functional analysis.

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Author information

Authors and Affiliations

  1. Max-Planck-Arbeitsgruppe, Universität Potsdam, FB Mathematik, Am Neuen Palais 10, PF 60 15 53, 14415, Potsdam, Germany

    Michael Demuth

  2. Department of Mathematics and Computer Sciences, Univ. Instelling Antwerp, Universitetsplein 1, 2610, Wilrijk/Antwerp, Belgium

    Jan van Casteren

Authors
  1. Michael Demuth
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  2. Jan van Casteren
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Editor information

Editors and Affiliations

  1. Technische Universität Clausthal, Institut für Mathematik, Erzstrasse 1, D-38678, Clausthal-Zellerfeld, Germany

    M. Demuth

  2. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Head Post Office Box 79, Moscow, Russia

    P. Exner

  3. Fachbereich Mathematik MA 7-2, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623, Berlin, Germany

    H. Neidhardt

  4. Université d’Aix-Marseille II et, Centre de Physique Théorique, CNRS — Luminy — Case 907, F-13288, Marseille Cedex 9, France

    V. Zagrebnov

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© 1994 Springer Basel AG

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Demuth, M., van Casteren, J. (1994). Framework and Results of Stochastic Spectral Analysis. In: Demuth, M., Exner, P., Neidhardt, H., Zagrebnov, V. (eds) Mathematical Results in Quantum Mechanics. Operator Theory: Advances and Applications, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8545-4_16

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  • DOI: https://doi.org/10.1007/978-3-0348-8545-4_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9673-3

  • Online ISBN: 978-3-0348-8545-4

  • eBook Packages: Springer Book Archive

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