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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


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.


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)


Vol.5 • No. 1 • 2014
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