Application of Nilpotent Approximation and the Orbit Method to the Search of the Diagonal Asymptotics of Sub-Riemannian Heat Kernels

Abstract

We propose a general scheme for the search of a fundamental solution to the hypoelliptic diffusion equation in a “sufficiently good” sub-Riemannian manifold and the small-time asymptotics for the solution, which includes the generalized Fourier transform and the orbit method closely related to it, as well as an application of the perturbative method to the nilpotent approximation, and Trotter’s formula.