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.
Cite this article
James D. Inglis, Spectral inequalities for operators on H-type groups. J. Spectr. Theory 2 (2012), no. 1, pp. 79–105DOI 10.4171/JST/22