Time-frequency analysis associated with k-Hankel-Wigner transforms
Commun. Korean Math. Soc. 2022 Vol. 37, No. 2, 521-535
Published online March 29, 2022
Printed April 30, 2022
Mohamed Amine Boubatra
Universit\'{e} 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 function 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
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