Asymptotics for the Heat Kernel on H-Type Groups

TL;DR

This paper provides precise asymptotic estimates for the heat kernel derivatives on H-type groups and applies these results to establish spectral discreteness of certain sub-Riemannian Ornstein-Uhlenbeck operators.

Contribution

It offers new sharp asymptotic estimates for the heat kernel derivatives on H-type groups and proves spectral discreteness of related operators.

Findings

Sharp asymptotic estimates for heat kernel derivatives

New proof of spectral discreteness for Ornstein-Uhlenbeck operators

Enhanced understanding of heat kernel behavior on H-type groups

Abstract

We give sharp asymptotic estimates at infinity of all radial partial derivatives of the heat kernel on H-type groups. As an application, we give a new proof of the discreteness of the spectrum of some natural sub-Riemannian Ornstein-Uhlenbeck operators on these groups.