Benedicks and Donoho-Stark type theorems

Authors: LOTFI KAMOUN, RAOUDHA LAFFI

Abstract: In this paper, we prove a Benedicks type theorem and a Donoho-Stark type theorem, for the generalized Fourier transform $\mathcal{F}_\alpha$ associated to some differential operators that we call Flensted-Jensen operators, in various spaces such $\mathrm{L}^1_\alpha(\mathbb{K})$, $\mathrm{L}^2_\alpha(\mathbb{K})$ and $\mathrm{L}^1_\alpha(\mathbb{K})\cap\mathrm{L}^2_\alpha(\mathbb{K})$, where $\mathbb{K}=\mathbb{R}_+\times\mathbb{R}$

Keywords: Generalized Fourier transform, Benedicks theorem, Donoho-Stark theorem, uncertainty principle

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