Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform
UDC 517.44 We introduce the windowed linear canonical Lions transform, which generalizes the classical Lions transform introduced in [K. Trimeche, Inversion of the Lions transmutation operators using generalized wavelets, Appl. Comput. Harmon. Anal., 4, № 1, 97–112 (1997)]. Some basic properties, s...
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| Date: | 2026 |
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| Main Authors: | , |
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| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9384 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1861046675592708096 |
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| author | Dades, Abdelaali Tyr, Othman Dades, Abdelaali Tyr, Othman |
| author_facet | Dades, Abdelaali Tyr, Othman Dades, Abdelaali Tyr, Othman |
| author_sort | Dades, Abdelaali |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
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| datestamp_date | 2026-03-29T12:33:29Z |
| description | UDC 517.44
We introduce the windowed linear canonical Lions transform, which generalizes the classical Lions transform introduced in [K. Trimeche, Inversion of the Lions transmutation operators using generalized wavelets, Appl. Comput. Harmon. Anal., 4, № 1, 97–112 (1997)]. Some basic properties, such as Plancherel, inversion, and convolution theorems involving this integral operator are formulated and proved. In addition, the Donoho–Stark uncertainty principle, the Lieb uncertainty principle, and the Heisenberg-type inequality via the $k$-entropy are discussed and proved for the proposed transform. |
| doi_str_mv | 10.3842/umzh.v78i3-4.9384 |
| first_indexed | 2026-03-29T01:00:29Z |
| format | Article |
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| id | umjimathkievua-article-9384 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-30T01:00:16Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-93842026-03-29T12:33:29Z Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform Dades, Abdelaali Tyr, Othman Dades, Abdelaali Tyr, Othman Linear canonical transform, Linear canonical Lions transform Generalized Fourier transform, Convolution theorem, Uncertainty principle kentropy Linear canonical transform, Linear canonical Lions transform, Generalized Fourier transform Convolution theorem, Uncertainty principle kentropy UDC 517.44 We introduce the windowed linear canonical Lions transform, which generalizes the classical Lions transform introduced in [K. Trimeche, Inversion of the Lions transmutation operators using generalized wavelets, Appl. Comput. Harmon. Anal., 4, № 1, 97–112 (1997)]. Some basic properties, such as Plancherel, inversion, and convolution theorems involving this integral operator are formulated and proved. In addition, the Donoho–Stark uncertainty principle, the Lieb uncertainty principle, and the Heisenberg-type inequality via the $k$-entropy are discussed and proved for the proposed transform. УДК 517.44 Теорема згортки та принципи невизначеності для віконного лінійного канонічного перетворення Ліонса Введено віконне лінійне канонічне перетворення Ліонса, яке узагальнює класичне перетворення Ліонса, наведене в K. Trimeche, Inversion of the Lions transmutation operators using generalized wavelets, Appl. Comput. Harmon. Anal., 4, № 1, 97–112 (1997)]. Наведено та доведено основні властивості цього інтегрального оператора, зокрема теореми Планшереля, обернення та згортки. Крім того, розглянуто та доведено принцип невизначеності Донохо–Старка, принцип невизначеності Ліба та нерівність типу Гейзенберга з використанням $k$-ентропії для запропонованого перетворення. Institute of Mathematics, NAS of Ukraine 2026-03-28 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9384 10.3842/umzh.v78i3-4.9384 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 3-4 (2026); 203–204 Український математичний журнал; Том 78 № 3-4 (2026); 203–204 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9384/10632 Copyright (c) 2026 Abdelaali Dades, Othman Tyr |
| spellingShingle | Dades, Abdelaali Tyr, Othman Dades, Abdelaali Tyr, Othman Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform |
| title | Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform |
| title_alt | Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform |
| title_full | Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform |
| title_fullStr | Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform |
| title_full_unstemmed | Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform |
| title_short | Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform |
| title_sort | convolution theorem and uncertainty principles for the windowed linear canonical lions transform |
| topic_facet | Linear canonical transform, Linear canonical Lions transform Generalized Fourier transform, Convolution theorem Uncertainty principle kentropy Linear canonical transform, Linear canonical Lions transform Generalized Fourier transform Convolution theorem Uncertainty principle kentropy |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9384 |
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