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Qualitative uncertainty principles for the hypergeometric Fourier transform

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Abstract

We prove an L pversion of the Donoho–Stark’s uncertainty principle for the hypergeometric Fourier transform on \({\mathbb{R}^d}\). Next, using the ultracontractive properties of the semigroups generated by the Heckman–Opdam Laplacian operator, we obtain an L p Heisenberg–Pauli–Weyl uncertainty principle for the hypergeometric Fourier transform on \({\mathbb{R}^d}\).

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  1. College of Sciences, Department of Mathematics, Taibah University, PO BOX 30002, Al Madinah AL Munawarah, Saudi Arabia

    H. Mejjaoli

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  1. H. Mejjaoli
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Correspondence to H. Mejjaoli.

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Dedicated to Khalifa Trimèche for his 68 birthday

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Mejjaoli, H. Qualitative uncertainty principles for the hypergeometric Fourier transform. Acta Math. Hungar. 145, 229–251 (2015). https://doi.org/10.1007/s10474-014-0466-5

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  • DOI: https://doi.org/10.1007/s10474-014-0466-5

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