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Time-frequency analysis associated with k-Hankel-Wigner transforms

Mohamed Amine Boubatra
대한수학회 (The Korean Mathematical Society)|2022.04|대한수학회논문집 (Communications of the KMS)|제37권 제2호|pp. 521-535|DOI 10.4134/CKMS.c210119

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키워드

k-Hankel transformk-Hankel-Wigner transformPlancherel's formulaHeisenberg's uncertainty principleCalder\'on's reproducing formulaextremal function
주제분류수학

초록

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.

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.

참고문헌 (25)

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