An integral representation for Folland's fundamental solution of the sub-Laplacian on Heisenberg groups $\Bbb{H}^{n}$

TL;DR

This paper presents a new integral representation for Folland's fundamental solution of the sub-Laplacian on Heisenberg groups by deriving it from the resolvent kernel, offering a novel analytical perspective.

Contribution

It introduces a new integral formula for the fundamental solution of the sub-Laplacian on Heisenberg groups based on the resolvent kernel, enhancing analytical tools.

Findings

Derived the fundamental solution from the resolvent kernel.

Provided a new integral representation for the fundamental solution.

Enhanced understanding of the sub-Laplacian on Heisenberg groups.

Abstract

We prove that the Folland's fundamental solution for the sub-Laplacian on Heisenberg groups can also be derived form the resolvent kernel of this sub-Laplacian. This provides us with a new integral representation for this fundamental solution.