01-289 F. Germinet, A. Klein

Operator kernel estimates for functions of generalized Schrodinger operators (309K, .ps) Jul 26, 01

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Abstract. We study the decay at large distances of operator kernels of functions of generalized Schr\"odinger operators, a class of semibounded second order partial differential operators of Mathematical Physics, which includes the Schr\"odinger operator, the magnetic Schr\"odinger 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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