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arXiv · 1710.02550

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

Joshua Campbell·Tai Melcher
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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.

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Joshua Campbell, Tai Melcher. 2017-10-06. Small-time asymptotics for subelliptic Hermite functions on $SU(2)$ and the CR sphere. https://doi.org/10.1007/s11118-019-09798-4

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