Operator kernel estimates for functions of generalized Schrödinger operators

Germinet, François; Klein, Abel

doi:10.1090/S0002-9939-02-06578-4

Operator kernel estimates for functions of generalized Schrödinger operators
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by François Germinet and Abel Klein

Proc. Amer. Math. Soc. 131 (2003), 911-920

DOI: https://doi.org/10.1090/S0002-9939-02-06578-4

Published electronically: July 17, 2002

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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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