Qualitative Uncertainty Principle for Gabor transform

TL;DR

This paper investigates the Qualitative Uncertainty Principle for Gabor transforms on various classes of locally compact groups, extending known results and establishing a weaker version for compact groups.

Contribution

It extends the Qualitative Uncertainty Principle for Gabor transform to new classes of groups and proves a weaker form for compact groups.

Findings

Qualitative Uncertainty Principle holds for abelian and certain non-abelian groups.

A weaker version of the principle is established for compact groups.

Results generalize the understanding of Gabor transform limitations across different group structures.

Abstract

We discuss the Qualitative Uncertainty Principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, $\mathbb{R}^n\times K$, $K \ltimes \mathbb{R}^n$ where $K$ is compact group. We shall also prove a weaker version of Qualitative Uncertainty Principle for Gabor transform in case of compact groups.