Department of Mathematics
Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator
© 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.
Asymptotic expansions, Grushin operator, Heat kernel, Heisenberg group, Saddle point method, Small-time asymptotics
Source Publication Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Royal Society, The
Link to Publisher's Edition
Chang, Der-Chen, and Yutian Li. "Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471.2175 (2015): 1-19.