Gaussian bounds of heat kernels for Schrödinger operators on Riemannian manifolds

Abstract

Suppose that the heat kernel on a complete Riemannian manifold satisfies global Gaussian bounds. We consider a Schrödinger operator for which the potential is a signed measure in a certain Kato class, and we establish a necessary and sufficient condition that the heat kernel of the Schrödinger operator also possesses the global Gaussian bounds.