Small-time asymptotics for subelliptic Hermite functions on $SU(2)$ and the CR sphere

Abstract

We show that, under a natural scaling, the small-time behavior of the logarithmic derivatives of the subelliptic heat kernel on $SU(2)$ converges to their analogues on the Heisenberg group at time 1. Realizing $SU(2)$ as ${\mathbb{S}}^3$, we then generalize these results to higher-order odd-dimensional spheres equipped with their natural subRiemannian structure, where the limiting spaces are now the higher-dimensional Heisenberg groups.

32 pages, corrected errors in preliminary estimates in Section 2.1

References in corpus (1)

• Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold