Geodesic
Dunkl-Gabor transform and time-frequency concentration
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 255-270

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The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg's uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks' uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with respect to a particular window function cannot be time-frequency concentrated in a subset of the form $S\times \mathcal B(0,b)$ in the time-frequency plane $\mathbb R^d\times \widehat {\mathbb R}^d$. As a side result we generalize a related result of Donoho and Stark on stable recovery of a signal which has been truncated and corrupted by noise.
The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg's uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks' uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with respect to a particular window function cannot be time-frequency concentrated in a subset of the form $S\times \mathcal B(0,b)$ in the time-frequency plane $\mathbb R^d\times \widehat {\mathbb R}^d$. As a side result we generalize a related result of Donoho and Stark on stable recovery of a signal which has been truncated and corrupted by noise.
DOI : 10.1007/s10587-015-0172-7
Classification : 42C20, 43A32, 46E22
Keywords: time-frequency concentration; Dunkl-Gabor transform; uncertainty principles 
Ghobber, Saifallah. Dunkl-Gabor transform and time-frequency concentration. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 255-270. doi: 10.1007/s10587-015-0172-7
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