Small-time asymptotics of hermite functions on compact symmetric spaces

Let M be a compact, connected, oriented Riemannian manifold. Hermite functi ons on M are defined in terms of the heat kernel, and the existence of an a symptotic expansion of these functions in powers of roott is established fo r small time. In the case where M is a compact symmetric spare, the asympto tic expansion of Hermite functions associated to "symmetrized" derivatives is shown to be greatly reduced, leaving an expansion in powers of t only. ( C) 2001 Academic Press.