Progressive Gelfand-Shilov Spaces and Wavelet Transforms

Progressive Gelfand-Shilov Spaces and Wavelet Transforms

We discuss progressive Gelfand-Shilov spaces consisting of analytic signals with almost exponential decay in time and frequency variables. It is shown that such signals enjoy an additional localization property. We define wavelet transform and inverse wavelet transform in (progressive) Gelfand-Shilo...

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Main Authors: Dušan Rakić, Nenad Teofanov
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2012/951819
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spelling doaj-1cc6953bc75540bd95b0fcf69cfd54bf2020-11-25T00:39:14ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/951819951819Progressive Gelfand-Shilov Spaces and Wavelet TransformsDušan Rakić0Nenad Teofanov1Faculty of Technology, University of Novi Sad, SerbiaDepartment of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, SerbiaWe discuss progressive Gelfand-Shilov spaces consisting of analytic signals with almost exponential decay in time and frequency variables. It is shown that such signals enjoy an additional localization property. We define wavelet transform and inverse wavelet transform in (progressive) Gelfand-Shilov spaces and study their continuity properties. It is shown that with a slightly faster decay in domain we may control the decay of the wavelet transform independently in each variable.http://dx.doi.org/10.1155/2012/951819
collection DOAJ
language English
format Article
sources DOAJ
author Dušan Rakić
Nenad Teofanov
spellingShingle Dušan Rakić
Nenad Teofanov
Progressive Gelfand-Shilov Spaces and Wavelet Transforms
Journal of Function Spaces and Applications
author_facet Dušan Rakić
Nenad Teofanov
author_sort Dušan Rakić
title Progressive Gelfand-Shilov Spaces and Wavelet Transforms
title_short Progressive Gelfand-Shilov Spaces and Wavelet Transforms
title_full Progressive Gelfand-Shilov Spaces and Wavelet Transforms
title_fullStr Progressive Gelfand-Shilov Spaces and Wavelet Transforms
title_full_unstemmed Progressive Gelfand-Shilov Spaces and Wavelet Transforms
title_sort progressive gelfand-shilov spaces and wavelet transforms
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
1758-4965
publishDate 2012-01-01
description We discuss progressive Gelfand-Shilov spaces consisting of analytic signals with almost exponential decay in time and frequency variables. It is shown that such signals enjoy an additional localization property. We define wavelet transform and inverse wavelet transform in (progressive) Gelfand-Shilov spaces and study their continuity properties. It is shown that with a slightly faster decay in domain we may control the decay of the wavelet transform independently in each variable.
url http://dx.doi.org/10.1155/2012/951819
work_keys_str_mv AT dusanrakic progressivegelfandshilovspacesandwavelettransforms
AT nenadteofanov progressivegelfandshilovspacesandwavelettransforms
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