An analogue of Ingham’s theorem on the Heisenberg group

Abstract

We prove an exact analogue of Ingham’s uncertainty principle for the group Fourier transform on the Heisenberg group. This is accomplished by explicitly constructing compactly supported functions on the Heisenberg group whose operator valued Fourier transforms have suitable Ingham type decay and proving an analogue of Chernoff’s theorem for the family of special Hermite operators.