Uncertainty Principles for Heisenberg Motion Group

Abstract

In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group $G={ℍ}^n⋊K$ , where $K=U\left(n\right)$ and ${ℍ}^n={ℂ}^n\times ℝ$ denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.