On theorems of Chernoff and Ingham on the Heisenberg group

TL;DR

This paper extends classical theorems of Chernoff and Ingham to the setting of the Heisenberg group, providing new insights into the behavior of the sublaplacian and Fourier transform in this non-commutative context.

Contribution

It introduces analogues of Chernoff's and Ingham's theorems specifically for the Heisenberg group, advancing harmonic analysis on this non-commutative structure.

Findings

Proved Chernoff's theorem analogue for the sublaplacian on the Heisenberg group

Established Ingham's theorem version for the Fourier transform on the Heisenberg group

Enhanced understanding of spectral properties in non-commutative harmonic analysis

Abstract

We prove an analogue of Chernoff's theorem for the sublaplacian on the Heisenberg group and use it prove a version of Ingham's theorem for the Fourier transform on the same group.