Uncertainty Principles for the Hankel-Gabor Transform

Abstract

In this paper, we prove an analogue of a time-frequency localization theorem for orthonormal sequences in $$L_{{\mu _\alpha }}^2({\mathbb{R}_ + })$$. As a consequence, we obtain an analogue of Shapiro’s Umbrella theorem for the Hankel-Gabor transform Vg. We also prove a mean dispersion inequality for Vg. Finally, we get a strong version of the uncertainty inequality for orthonormal sequences of $$L_{{\mu _\alpha }}^2({\mathbb{R}_ + })$$.