Beurling's theorem on the Heisenberg group

TL;DR

This paper extends Beurling's theorem to the Fourier transform on the Heisenberg group, leading to new versions of Hardy and Cowling-Price theorems in this non-commutative setting.

Contribution

It formulates and proves an analogue of Beurling's theorem specifically for the Fourier transform on the Heisenberg group, a significant extension of classical harmonic analysis.

Findings

Established Beurling's theorem analogue for the Heisenberg group Fourier transform

Derived Hardy and Cowling-Price theorems as corollaries

Enhanced understanding of harmonic analysis on non-commutative groups

Abstract

We formulate and prove an analogue of Beurling's theorem for the Fourier transform on the Heisenberg group. As a consequence we deduce Hardy and Cowling-Price theorems.