Spectral inequalities for operators on H-type groups

Abstract

In this paper the spectra of certain Schrödinger-type operators defined in the sub-elliptic setting of H-type groups are investigated. Two approaches are taken: the first one makes use of a convenient unitary transformation on the Heisenberg group, while the second proceeds via functional inequalities. The paper concludes by highlighting a major difference between the spectrum of the considered operators depending on which natural sub-Riemannian metric is chosen.