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Small-Time Asymptotics for Subelliptic Hermite Functions on SU(2) and the CR Sphere

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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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Acknowledgements

We thank the anonymous referee for valuable feedback that improved the paper, and in particular for identifying an error in an earlier version.

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Authors and Affiliations

  1. Ixonia, WI, USA

    Joshua Campbell

  2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, USA

    Tai Melcher

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  1. Joshua Campbell
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  2. Tai Melcher
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Correspondence to Tai Melcher.

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Both authors were supported in part by NSF DMS 1255574.

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Campbell, J., Melcher, T. Small-Time Asymptotics for Subelliptic Hermite Functions on SU(2) and the CR Sphere. Potential Anal 53, 1063–1095 (2020). https://doi.org/10.1007/s11118-019-09798-4

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  • DOI: https://doi.org/10.1007/s11118-019-09798-4

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