$\mathcal{O}_α$-transformation and its uncertainty principles
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908869283807232 |
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| author | Minh, Lai Tien Tuan, Trinh |
| author_facet | Minh, Lai Tien Tuan, Trinh |
| contents | In this paper, we introduce a family of integral transforms, denoted by \(\mathcal{O}_α\), and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle \(α\notin π\mathbb{Z}\). We demonstrate that the \(\mathcal{O}_α\)-transformation constitutes a well-defined integral operator by establishing its basic operational properties. Besides, we survey various mathematical aspects of the uncertainty principles for the $\mathcal{O}_α$-transform, including Heisenberg's inequality, logarithmic uncertainty inequality, local uncertainty inequality, Hardy's inequality, Pitt's inequality, and Beurling-H{ö}rmander's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{O}_α$-transformation and its uncertainty principles Minh, Lai Tien Tuan, Trinh Classical Analysis and ODEs Functional Analysis 43A32, 42A38, 42B10, 26D10 In this paper, we introduce a family of integral transforms, denoted by \(\mathcal{O}_α\), and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle \(α\notin π\mathbb{Z}\). We demonstrate that the \(\mathcal{O}_α\)-transformation constitutes a well-defined integral operator by establishing its basic operational properties. Besides, we survey various mathematical aspects of the uncertainty principles for the $\mathcal{O}_α$-transform, including Heisenberg's inequality, logarithmic uncertainty inequality, local uncertainty inequality, Hardy's inequality, Pitt's inequality, and Beurling-H{ö}rmander's theorem. |
| title | $\mathcal{O}_α$-transformation and its uncertainty principles |
| topic | Classical Analysis and ODEs Functional Analysis 43A32, 42A38, 42B10, 26D10 |
| url | https://arxiv.org/abs/2503.15132 |