International Conference Harmonic analysis and approximations, IV , 2008-09-19

Title : ( Concentration and stable reconstruction of continuous Gabo Transform )

Authors: Rajab Ali Kamyabi Gol , Arash Ghaani Farashahi ,

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In this article we generalize some uncertainty principles related with the continuous Gabor transform for strong commutative hypergroups. More precisely, in the following we prove that for a locally compact strong commutative hypergroup X with the Haar measure µ and the Plancherel measure λ on its dual X, window function ψ and each f ∈ L2(X), the portion of Gψ f lying outside some small U of finite µ × λ- measure in X × X cannot be arbitrary small, either. For sufficiently small U, this can be seen immediately by estimating the Hilbert-Schmidt norm of a suitable defined operator. Also we generalize the stable reconstruction of Gabor transform from incomplete noisy data, for strong commutative hypergroups. As an example we show how these techniques apply to the Locally compact groups and Bessel−Kingman hypergroups.

Keywords

, Gabor transform, Haar measure, Plancherel measure, Hilbert-Schmidt
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@inproceedings{paperid:1006852,
author = {Kamyabi Gol, Rajab Ali and Ghaani Farashahi, Arash},
title = {Concentration and stable reconstruction of continuous Gabo Transform},
booktitle = {International Conference Harmonic analysis and approximations, IV},
year = {2008},
keywords = {Gabor transform; Haar measure; Plancherel measure; Hilbert-Schmidt norm},
}

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%0 Conference Proceedings
%T Concentration and stable reconstruction of continuous Gabo Transform
%A Kamyabi Gol, Rajab Ali
%A Ghaani Farashahi, Arash
%J International Conference Harmonic analysis and approximations, IV
%D 2008

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