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SHORT-TIME ASYMPTOTICS OF HEAT KERNELS FOR A CLASS OF HYPOELLIPTIC OPERATORS

By R. W. Brockett and A. Mansouri

Abstract

Abstract. We compute the short-time asymptotics of heat kernels for a family of hypoelliptic operators, and we relate these to the value function of an associated variational problem previously investigated in the control theory literature. These heat kernels generalize to the noncontact case a heat kernel that has been previously obtained for the contact hypoelliptic Laplacian defined on the Heisenberg group. 1. Introduction. In his seminal paper, Gaveau [7] constructed the heat kernel for the sub-elliptic Laplacian on the Heisenberg group. In a series of recent papers, Beals et al. [1], [2], [3] have rederived this result and computed heat kernels for sub-elliptic Laplacians for both contact and noncontact geometries by relating the heat kernels to an underlying complex Hamiltonian mechanic

Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.417.8989
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