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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

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

Language

English

Abstract

© 2015 The Author(s) Published by the Royal Society. All rights reserved. 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.

Keywords

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

Publication Date

2015

Source Publication Title

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

Volume

471

Issue

2175

Start Page

1

End Page

19

Publisher

Royal Society, The

ISSN (print)

13645021

ISSN (electronic)

14712946

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