Heisenberg Uncertainty Inequality for Gabor Transform

TL;DR

This paper extends the Heisenberg uncertainty inequality to Gabor transforms on certain semidirect product groups, broadening the understanding of uncertainty principles in harmonic analysis.

Contribution

It proves the Heisenberg uncertainty inequality for Gabor transforms on groups of the form K ⋉ ℝ^n, where K is a separable unimodular locally compact group of type I.

Findings

Heisenberg inequality established for these groups

Gabor transform uncertainty bounds derived for multiple group classes

Advances harmonic analysis on semidirect product groups

Abstract

We discuss Heisenberg uncertainty inequality for groups of the form $K \ltimes \mathbb{R}^n$, $K$ is a separable unimodular locally compact group of type I. This inequality is also proved for Gabor transform for several classes of groups of the form $K \ltimes \mathbb{R}^n$.