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Czechoslovak Mathematical Journal

, Volume 65, Issue 1, pp 255–270 | Cite as

Dunkl-Gabor transform and time-frequency concentration

  • Saifallah Ghobber
Article

Abstract

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 × B(0, b) in the time-frequency plane ℝ d × ℝ̂ 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.

Keywords

time-frequency concentration Dunkl-Gabor transform uncertainty principles 

MSC 2010

42C20 43A32 46E22 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  1. 1.Faculté des Sciences de Tunis, LR11ES11 Analyse Mathématiques et ApplicationsUniversité de Tunis El ManarTunisTunisia

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