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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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9384 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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| DOI: | 10.3842/umzh.v78i3-4.9384 |