J. Aust. Math. Soc.
78 (2005), 109147

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 nonzero positive quasiinvariant 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.

Download the article in PDF format (size 336 Kb)


