Analogues of theorems of Chernoff and Ingham on the Heisenberg group

Abstract

We prove an analogue of Chernoff's theorem for the Laplacian ${\Delta }_{\mathbb{H}}$ on the Heisenberg group ${\mathbb{H}}^n.$ As an application, we prove Ingham type theorems for the group Fourier transform on ${\mathbb{H}}^n$ and also for the spectral projections associated to the sublaplacian.

20 pages