Small-Time Asymptotics of Hermite Functions on Compact Symmetric Spaces1

Let M be a compact, connected, oriented Riemannian manifold. Hermite functions on M are defined in terms of the heat kernel, and the existence of an asymptotic expansion of these functions in powers of √t is established for small time. In the case where M is a compact symmetric space, the asymptotic expansion of Hermite functions associated to “symmetrized” derivatives is shown to be greatly reduced, leaving an expansion in powers of t only