New results on the continuous Weinstein wavelet transform

We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text] . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavele...

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Autores principales: Mejjaoli, Hatem, Ould Ahmed Salem, Ahmedou
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5660847/
https://www.ncbi.nlm.nih.gov/pubmed/29142483
http://dx.doi.org/10.1186/s13660-017-1534-5
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author Mejjaoli, Hatem
Ould Ahmed Salem, Ahmedou
author_facet Mejjaoli, Hatem
Ould Ahmed Salem, Ahmedou
author_sort Mejjaoli, Hatem
collection PubMed
description We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text] . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of [Formula: see text] on sets of finite measure. In particular, Benedicks-type and Donoho-Stark’s uncertainty principles are given. Finally, we prove many versions of Heisenberg-type uncertainty principles for [Formula: see text] .
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spelling pubmed-56608472017-11-13 New results on the continuous Weinstein wavelet transform Mejjaoli, Hatem Ould Ahmed Salem, Ahmedou J Inequal Appl Research We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text] . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of [Formula: see text] on sets of finite measure. In particular, Benedicks-type and Donoho-Stark’s uncertainty principles are given. Finally, we prove many versions of Heisenberg-type uncertainty principles for [Formula: see text] . Springer International Publishing 2017-10-28 2017 /pmc/articles/PMC5660847/ /pubmed/29142483 http://dx.doi.org/10.1186/s13660-017-1534-5 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Mejjaoli, Hatem
Ould Ahmed Salem, Ahmedou
New results on the continuous Weinstein wavelet transform
title New results on the continuous Weinstein wavelet transform
title_full New results on the continuous Weinstein wavelet transform
title_fullStr New results on the continuous Weinstein wavelet transform
title_full_unstemmed New results on the continuous Weinstein wavelet transform
title_short New results on the continuous Weinstein wavelet transform
title_sort new results on the continuous weinstein wavelet transform
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5660847/
https://www.ncbi.nlm.nih.gov/pubmed/29142483
http://dx.doi.org/10.1186/s13660-017-1534-5
work_keys_str_mv AT mejjaolihatem newresultsonthecontinuousweinsteinwavelettransform
AT ouldahmedsalemahmedou newresultsonthecontinuousweinsteinwavelettransform

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