A new class of uncertainty principles for the Gabor transform

Abstract

The aim of this paper is to formulate a new class of uncertainty principles for the classical Gabor transform in [Formula: see text]. To begin with, we formulate a couple of concentration-based uncertainty principles, including the Benedick–Amrein–Berthier and the local-type uncertainty inequalities for the Gabor transform. Second, we derive several unique weighted uncertainty inequalities, such as the Pitt’s and Beckner’s inequalities for the Gabor transforms on [Formula: see text]. Besides, the logarithmic Sobolev-type principles for the Gabor transforms are established at the end.