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Optimal heat kernel estimates for schrödinger operators with magnetic fields in two dimensions

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Abstract

Sharp smoothing estimates are proven for magnetic Schrödinger semigroups in two dimensions under the assumption that the magnetic field is bounded below by some positive constantB 0. As a consequence theL∞ norm of the associated integral kernel is bounded by theL∞ norm of the Mehler kernel of the Schrödinger semigroup with the constant magnetic fieldB 0.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA

    Michael Loss

  2. Institut fur Mathematik, Universitat Graz, A-8010, Graz, Austria

    Bernd Thaller

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  1. Michael Loss
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  2. Bernd Thaller
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© {dy1996} by the authors Reproduction of this article, in its entirety, by any means is permitted for noncommercial purposes

Work supported by N S F grant DMS-95-00840 and the Erwin Schrödinger Institute

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Loss, M., Thaller, B. Optimal heat kernel estimates for schrödinger operators with magnetic fields in two dimensions. Commun. Math. Phys. 186, 95–107 (1997). https://doi.org/10.1007/BF02885674

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  • DOI: https://doi.org/10.1007/BF02885674

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