On the method of differentiation and its application to asymptotics for the heat kernel on H-type groups

TL;DR

This paper develops a generalized method for differentiating asymptotic expansions and applies it to derive sharp asymptotic estimates of the heat kernel on H-type groups, extending results from isotropic Heisenberg groups.

Contribution

It introduces a generalized differentiation method for asymptotic expansions and applies it to obtain precise heat kernel estimates on H-type groups.

Findings

Established conditions for differentiating asymptotic sequences.

Derived sharp asymptotic estimates of the heat kernel on H-type groups.

Extended results from isotropic Heisenberg groups to H-type groups.

Abstract

The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes it. As an application, our second aim is to give sharp asymptotic estimates at infinity of the heat kernel on H-type groups by the method of differentiation provided we have the result of the isotropic Heisenberg groups.