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http://dx.doi.org/10.4134/CKMS.c210119

TIME-FREQUENCY ANALYSIS ASSOCIATED WITH K-HANKEL-WIGNER TRANSFORMS  

Boubatra, Mohamed Amine (Laboratoire d'Analyse Mathematique et Applications LR11ES11 Faculte des Sciences de Tunis Universite Tunis El Manar)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.2, 2022 , pp. 521-535 More about this Journal
Abstract
In this paper, we introduce the k-Hankel-Wigner transform on 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 Calderón'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; Calderon's reproducing formula; extremal function;
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