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

Der Chen Chang, Yutian LI*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 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 languageEnglish
Article number20140943
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume471
Issue number2175
DOIs
Publication statusPublished - 8 Mar 2015

Scopus Subject Areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

User-Defined Keywords

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

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