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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Operator kernel estimates for functions of generalized Schrödinger operators
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by François Germinet and Abel Klein PDF
Proc. Amer. Math. Soc. 131 (2003), 911-920 Request permission

Abstract:

We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of mathematical physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved Combes-Thomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than any polynomial.
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Additional Information
  • François Germinet
  • Affiliation: UMR 8524 CNRS, UFR de Mathématiques, Université de Lille 1, F-59655 Villeneuve d’Ascq Cédex, France
  • Email: germinet@agat.univ-lille1.fr
  • Abel Klein
  • Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
  • MR Author ID: 191739
  • Email: aklein@uci.edu
  • Received by editor(s): July 18, 2001
  • Received by editor(s) in revised form: October 22, 2001
  • Published electronically: July 17, 2002
  • Additional Notes: The second author was supported in part by NSF Grants DMS-9800883 and DMS-9800860
  • Communicated by: Joseph A. Ball
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 911-920
  • MSC (1991): Primary 81Q10, 47F05; Secondary 35P05
  • DOI: https://doi.org/10.1090/S0002-9939-02-06578-4
  • MathSciNet review: 1937430