Korean J. Math. Vol. 23 No. 1 (2015) pp.129-151
DOI: https://doi.org/10.11568/kjm.2015.23.1.129

Qualitative uncertainty principles for the inverse of the hypergeometric fourier transform

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Published: Mar 30, 2015
Keywords:
Hypergeometric Fourier transform, Donoho-Stark's uncertainty principle, $L^{p}$ Heisenberg-Pauli-Weyl uncertainty principle
Mathematics Subject Classification:
42B10, 42B30, 43A32

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

Abstract

In this paper, we prove an $L^{p}$ version of Donoho-Stark's uncertainty principle for the inverse of 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 inverse of the hypergeometric Fourier transform on $\mathbb{R}^{d}$.


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Supporting Agencies

This paper is dedicated to Professor Khalifa Trim\`{e}che on the occasion of his promotion to Professor Emeritus.

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