Spectral Properties of the Sub-Laplacian on 2-step Stratified Lie Groups without the Moore-Wolf Condition

Abstract

In this paper, we consider the structure of the $L^2-$spectrum of the sub-Laplacian on 2-step stratified Lie groups by using the theory of unitary irreducible representations and Hermit functions. We extend the results for Heisenberg group and H-type Lie group to more general 2-step stratified Lie groups without the Moore-Wolf condition.