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Small-Time Asymptotics for Subelliptic Hermite Functions on SU(2) and the CR Sphere
- Source :
- Potential Analysis. 53:1063-1095
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
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.<br />32 pages, corrected errors in preliminary estimates in Section 2.1
- Subjects :
- Functional analysis
010102 general mathematics
Structure (category theory)
16. Peace & justice
01 natural sciences
Potential theory
010104 statistics & probability
Mathematics - Analysis of PDEs
FOS: Mathematics
Heisenberg group
Logarithmic derivative
0101 mathematics
Scaling
Analysis
Special unitary group
Heat kernel
Analysis of PDEs (math.AP)
Mathematics
Mathematical physics
Subjects
Details
- ISSN :
- 1572929X and 09262601
- Volume :
- 53
- Database :
- OpenAIRE
- Journal :
- Potential Analysis
- Accession number :
- edsair.doi.dedup.....8855fb1507c96a624111915467137c09