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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/951819 |
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| _version_ | 1849307218918244352 |
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| author | Dušan Rakić Nenad Teofanov |
| author_facet | Dušan Rakić Nenad Teofanov |
| author_sort | Dušan Rakić |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-1cc6953bc75540bd95b0fcf69cfd54bf |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-1cc6953bc75540bd95b0fcf69cfd54bf2025-08-20T03:54:51ZengWileyJournal 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 |
| spellingShingle | Dušan Rakić Nenad Teofanov Progressive Gelfand-Shilov Spaces and Wavelet Transforms Journal of Function Spaces and Applications |
| title | 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_short | Progressive Gelfand-Shilov Spaces and Wavelet Transforms |
| title_sort | progressive gelfand shilov spaces and wavelet transforms |
| url | http://dx.doi.org/10.1155/2012/951819 |
| work_keys_str_mv | AT dusanrakic progressivegelfandshilovspacesandwavelettransforms AT nenadteofanov progressivegelfandshilovspacesandwavelettransforms |