Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator

Der Chen Chang; Yutian Li

doi:10.1098/rspa.2014.0943

Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator

Der Chen Chang, Yutian Li^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

5 Citations (Scopus)

Abstract

The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries.

Original language	English
Article number	20140943
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	471
Issue number	2175
DOIs	https://doi.org/10.1098/rspa.2014.0943
Publication status	Published - 8 Mar 2015

User-Defined Keywords

Asymptotic expansions
Grushin operator
Heat kernel
Heisenberg group
Saddle point method
Small-time asymptotics

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10.1098/rspa.2014.0943

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abstract = "The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries.",

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N2 - The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries.

AB - The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries.

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KW - Grushin operator

KW - Heat kernel

KW - Heisenberg group

KW - Saddle point method

KW - Small-time asymptotics

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JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator

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