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Fall 2000 Estimates of global bounds for some Schrödinger heat kernels on manifolds
Qi S. Zhang, Z. Zhao
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Illinois J. Math. 44(3): 556-573 (Fall 2000). DOI: 10.1215/ijm/1256060416


We establish global bounds for the heat kernel of Schrödinger operators $-\Delta + V$ where $V$ is a certain long range potential. As a consequence we find some conditions for the heat kernel to have global Gaussian lower and upper bound. Some of the conditions are sharp if the potential does not change sign. We also provide a generalized Liouville theorem for Schrödinger operators and a refined version of the trace formula of Sa Barreto and Zworski [SZ].


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Qi S. Zhang. Z. Zhao. "Estimates of global bounds for some Schrödinger heat kernels on manifolds." Illinois J. Math. 44 (3) 556 - 573, Fall 2000.


Published: Fall 2000
First available in Project Euclid: 20 October 2009

zbMATH: 0985.35016
MathSciNet: MR1772429
Digital Object Identifier: 10.1215/ijm/1256060416

Primary: 58J35
Secondary: 35B45 , 35K05

Rights: Copyright © 2000 University of Illinois at Urbana-Champaign


Vol.44 • No. 3 • Fall 2000
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