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arXiv · 2601.14890

Quadratic-Phase Fourier--Bessel Transform: definitions, properties and uncertainty principles

Ahmed Saoudi
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Abstract

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.

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Ahmed Saoudi. 2026-01-21. Quadratic-Phase Fourier--Bessel Transform: definitions, properties and uncertainty principles. https://arxiv.org/abs/2601.14890

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