Quadratic-Phase Fourier--Bessel Transform: definitions, properties and uncertainty principles
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908779716542464 |
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| author | Saoudi, Ahmed |
| author_facet | Saoudi, Ahmed |
| contents | In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated translation operator and convolution product, establishing their main properties within this framework. As an application, we prove a Donoho-Stark-type uncertainty principle for the quadratic-phase Fourier--Bessel transform, extending classical uncertainty results to this generalized setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14890 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quadratic-Phase Fourier--Bessel Transform: definitions, properties and uncertainty principles Saoudi, Ahmed Mathematical Physics In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated translation operator and convolution product, establishing their main properties within this framework. As an application, we prove a Donoho-Stark-type uncertainty principle for the quadratic-phase Fourier--Bessel transform, extending classical uncertainty results to this generalized setting. |
| title | Quadratic-Phase Fourier--Bessel Transform: definitions, properties and uncertainty principles |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.14890 |