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2014 $L^p$ Donoho-Stark Uncertainty Principles for the Dunkl Transform on ${\mathbb{R}^{\text{d}}}$
Fethi Soltani
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J. Phys. Math. 5(1): 1-4 (2014). DOI: 10.4172/2090-0902.1000127

Abstract

In the Dunkl setting, we establish three continuous uncertainty principles of concentration type, where the sets of concentration are not intervals. The first and the second uncertainty principles are $L^p$ versions and depend on the sets of concentration $T$ and $W$, and on the time function $f$. The time-limiting operators and the Dunkl integral operators play an important role to prove the main results presented in this paper. However, the third uncertainty principle is also $L^p$ version depends on the sets of concentration and he is independent on the band limited function $f$. These uncertainty principles generalize the results obtained for the Fourier transform and the Dunkl transform in the case $p=2$.

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Fethi Soltani. "$L^p$ Donoho-Stark Uncertainty Principles for the Dunkl Transform on ${\mathbb{R}^{\text{d}}}$." J. Phys. Math. 5 (1) 1 - 4, 2014. https://doi.org/10.4172/2090-0902.1000127

Information

Published: 2014
First available in Project Euclid: 23 July 2015

zbMATH: 1327.42012
Digital Object Identifier: 10.4172/2090-0902.1000127

Keywords: Concentration uncertainty principles , Dunkl integral operators , Dunkl transform

Rights: Copyright © 2014 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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Vol.5 • No. 1 • 2014
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