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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Operator kernel estimates for functions of generalized Schrödinger operators


Authors: François Germinet and Abel Klein
Journal: Proc. Amer. Math. Soc. 131 (2003), 911-920
MSC (1991): Primary 81Q10, 47F05; Secondary 35P05
Published electronically: July 17, 2002
MathSciNet review: 1937430
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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
Email: aklein@uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06578-4
PII: S 0002-9939(02)06578-4
Keywords: Schr\"odinger operator, magnetic Schr\"odinger operator, classical wave operator, acoustic operator, Maxwell operator, Combes-Thomas estimate
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
Article copyright: © Copyright 2002 American Mathematical Society