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Bulletin of the London Mathematical Society Advance Access originally published online on December 15, 2006
Bulletin of the London Mathematical Society 2007 39(1):85-94; doi:10.1112/blms/bdl016
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© 2006 London Mathematical Society

Gaussian bounds of heat kernels for Schrödinger operators on Riemannian manifolds

Masayoshi Takeda

Mathematical Institute
Tohoku University
Aoba, Sendai, 980-8578
Japan
takeda{at}math.tohoku.ac.jp

Received 2 May 2005. Revision received 17 January 2006.

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.


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