Uncertainty Principles for the Hankel-Gabor Transform

Aymen Hammami ()
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Aymen Hammami: SAMM EA 4543, Université Paris 1 Panthéon-Sorbonne, Fédération CNRS FP2M

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 251-264

Abstract: 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 $$L_{{\mu _\alpha }}^2({\mathbb{R}_ + })$$.

Keywords: Uncertainty inequality; The windowed Hankel transform; time-frequency localization theorem; mean dispersion inequality; 42A38; 44A35 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0398-4

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