Integrated density of states for the sub-Laplacian on Heisenberg groups

TL;DR

This paper rederives the integrated density of states for the sub-Laplacian on Heisenberg groups using the resolvent kernel, providing a new perspective on spectral analysis in sub-Riemannian geometry.

Contribution

It introduces a novel derivation method for the integrated density of states of the sub-Laplacian on Heisenberg groups via the resolvent kernel.

Findings

Explicit expression for the integrated density of states derived

New method simplifies spectral analysis on Heisenberg groups

Potential applications in quantum mechanics and geometric analysis

Abstract

We rederive the expression of the integrated density of states for \ the sub-Laplacian on Heisenberg groups $\mathbb{H}_{n}$ by using its resolvent kernel.