Time-frequency analysis associated with k-Hankel-Wigner transforms
Commun. Korean Math. Soc.
Published online November 18, 2021
Mohamed Amine Boubatra
University of Tunis El Manar
Abstract : In this paper, we introduce the k-Hankel-Wigner transform on $\mathbb{R}$ in some problems of
time-frequency analysis. As a first point, we present some
harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for
this transform. next we prove a Heisenberg's uncertainty principle and a Calder\'on's reproducing formula for this transform. We conclude this paper by studying an extremal functions for this transform.
Keywords : k-Hankel transform, k-Hankel-Wigner transform, Plancherel's formula, Heisenberg's uncertainty principle, Calder\'on's reproducing formula, extremal function
MSC numbers : 42B10, 44A20, 46F12
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