J. Aust. Math. Soc.  78 (2005), 109-147
Heat kernels on homogeneous spaces

 C. M. P. A. Smulders   Department of Mathematics and Comp. Sci.   Eindhoven University of Technology   P.O. Box 513   5600 MB Eindhoven   The Netherlands  camsmul@cs.com

Abstract
Let be a basis of the Lie algebra of a connected Lie group and let be a Lie subgroup of . If is a non-zero positive quasi-invariant regular Borel measure on the homogeneous space and is a continuous cocycle, then under a rather weak condition on and there exists in a natural way a (weakly*) continuous representation of in for all . Let be the infinitesimal generator with respect to and the direction for all . We consider -th order strongly elliptic operators with complex coefficients . We show that the semigroup generated by the closure of has a reduced heat kernel and we derive upper bounds for and all its derivatives.