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

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

We show that, under a natural scaling, the small-time behavior of the logarithmic derivatives of the subelliptic heat kernel on S U (2) converges to their analogues on the Heisenberg group at time 1. Realizing S U (2) as S 3 , we then generalize these results to higher-order odd-dimensional spheres...

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Veröffentlicht in:Potential analysis 2020-10, Vol.53 (3), p.1063-1095
Hauptverfasser: Campbell, Joshua, Melcher, Tai
Format: Artikel
Sprache:eng
Schlagworte:
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
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Zusammenfassung:We show that, under a natural scaling, the small-time behavior of the logarithmic derivatives of the subelliptic heat kernel on S U (2) converges to their analogues on the Heisenberg group at time 1. Realizing S U (2) as 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.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-019-09798-4