Localization Operators for the Linear Canonical Dunkl Windowed Transformation
One of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the linear canonical Dunkl transform, we introduc...
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MDPI AG
2025-03-01
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| author | Saifallah Ghobber Hatem Mejjaoli |
| author_facet | Saifallah Ghobber Hatem Mejjaoli |
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| description | One of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the linear canonical Dunkl transform, we introduce and then study the linear canonical Dunkl windowed transform (LCDWT). Given that localization operators are both theoretically and practically relevant, we will focus in this paper on a number of time–frequency analysis topics for the LCDWT, such as the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula> boundedness and compactness of localization operators for the LCWGT. Then, we study their trace class characterization and show that they are in the Schatten–von Neumann classes. Then, we study their spectral properties in order to give some results on the spectrograms for the LCDWT. |
| format | Article |
| id | doaj-art-0143b7dca67744abae1c08cf4ce51416 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-0143b7dca67744abae1c08cf4ce514162025-08-20T03:14:20ZengMDPI AGAxioms2075-16802025-03-0114426210.3390/axioms14040262Localization Operators for the Linear Canonical Dunkl Windowed TransformationSaifallah Ghobber0Hatem Mejjaoli1Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi ArabiaDepartment of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al Madinah Al Munawarah 42353, Saudi ArabiaOne of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the linear canonical Dunkl transform, we introduce and then study the linear canonical Dunkl windowed transform (LCDWT). Given that localization operators are both theoretically and practically relevant, we will focus in this paper on a number of time–frequency analysis topics for the LCDWT, such as the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula> boundedness and compactness of localization operators for the LCWGT. Then, we study their trace class characterization and show that they are in the Schatten–von Neumann classes. Then, we study their spectral properties in order to give some results on the spectrograms for the LCDWT.https://www.mdpi.com/2075-1680/14/4/262Dunkl transformlinear canonical transformgeneralized translationgeneralized convolutiongeneralized windowed transformlocalization operators |
| spellingShingle | Saifallah Ghobber Hatem Mejjaoli Localization Operators for the Linear Canonical Dunkl Windowed Transformation Axioms Dunkl transform linear canonical transform generalized translation generalized convolution generalized windowed transform localization operators |
| title | Localization Operators for the Linear Canonical Dunkl Windowed Transformation |
| title_full | Localization Operators for the Linear Canonical Dunkl Windowed Transformation |
| title_fullStr | Localization Operators for the Linear Canonical Dunkl Windowed Transformation |
| title_full_unstemmed | Localization Operators for the Linear Canonical Dunkl Windowed Transformation |
| title_short | Localization Operators for the Linear Canonical Dunkl Windowed Transformation |
| title_sort | localization operators for the linear canonical dunkl windowed transformation |
| topic | Dunkl transform linear canonical transform generalized translation generalized convolution generalized windowed transform localization operators |
| url | https://www.mdpi.com/2075-1680/14/4/262 |
| work_keys_str_mv | AT saifallahghobber localizationoperatorsforthelinearcanonicaldunklwindowedtransformation AT hatemmejjaoli localizationoperatorsforthelinearcanonicaldunklwindowedtransformation |