Sharp Gaussian estimates for Schrödinger heat kernels: $L^p$ integrability conditions

Published 23 Nov 2015 in math.FA and math.AP | (1511.07167v3)

Abstract: We give new sufficient conditions for comparability of the fundamental solution of the Schr\"odinger equation $\partial_t=\Delta+V$ with the Gauss-Weierstrass kernel and show that local $L^p$ integrability of $V$ for $p> 1$ is not necessary for the comparability.

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