Uncertainty principles for the $q$-Hankel–Stockwell transform
UDC 517.3 By using the $q$-Jackson integral and some elements of the $q$-harmonic analysis associated with the $q$-Hankel transform, we introduce and study a $q$-analog of the Hankel–Stockwell transform. We give some harmonic analysis properties (Plancherel formula, inversion formula, r...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7166 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.3
By using the $q$-Jackson integral and some elements of the $q$-harmonic analysis associated with the $q$-Hankel transform, we introduce and study a $q$-analog of the Hankel–Stockwell transform. We give some harmonic analysis properties (Plancherel formula, inversion formula, reproduicing kernel, etc.).  Furthermore, we establish a version of Heisenberg's uncertainty principles. Finally, we study the $q$-Hankel–Stockwell transform on a subset of finite measure. |
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| DOI: | 10.37863/umzh.v75i7.7166 |