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Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle
-
Hichem Ben Aouicha
and
Chirine Chettaoui
Published/Copyright:
March 27, 2012
Abstract.
In this work, by using the Dunkl transform operator, we extend the Donoho–Stark uncertainty principle to this transform. A special interest is devoted to the computation of the spectrum of the finite Dunkl transform. For this purpose, we develop two different practical methods. Also, we show how the eigenfunctions of the finite Dunkl transform can be used to reconstruct in a stable way the Dunkl bandlimited signals. Finally, we present some numerical examples that illustrate the results of this work.
Keywords.: Dunkl transform; Donoho–Stark uncertainty principle; finite Dunkl transform; numerical computation of the spectrum; Dunkl bandlimited signals
Received: 2010-12-25
Revised: 2011-06-29
Published Online: 2012-03-27
Published in Print: 2012-April
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Dunkl transform;
Donoho–Stark uncertainty principle;
finite Dunkl transform;
numerical computation of the spectrum;
Dunkl bandlimited signals
Articles in the same Issue
- Masthead
- Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle
- A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
- Combined Sundman–Darboux transformations and solutions of nonlinear ordinary differential equations of second order
- Multiresolution analysis on local fields and characterization of scaling functions
- Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions
- Small gaps Fourier series and generalized variations
- Central limit theorems for radial random walks on matrices for
