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.

中文翻译：

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SU（2）和CR球面上亚椭圆形Hermite函数的小渐近性

我们显示，在自然尺度下，S U（2）上亚椭圆形热核的对数导数的小时间行为在时间1处收敛到海森堡群上的类似物。实现S U（2）为\（ \ mathbb {S} ^ {3} \），然后将这些结果推广到配备其自然亚黎曼结构的高阶奇维球体，其中的限制空间现在是高维Heisenberg群。