On the Structure of Uncertainty Inequalities for the Novel Quadratic-Phase Deformed Hankel Transform

Quadratic-phase (deformed) transforms are a recent extension within the class of linear canonical transformations and have attracted increasing interest in signal analysis and related fields. Motivated by the fundamental role of uncertainty principles in theoretical analysis and practical applications, this article presents a thorough study of the uncertainty inequalities associated with the quadratic-phase deformed Hankel transform (QPDHT), which has recently been introduced into the literature. We first establish qualitative results. We then derive several forms of the Heisenberg’s uncertainty inequality using different analytical approaches, highlighting the interplay between spatial and frequency localization. Finally, we complete our study by proving local uncertainty inequalities, which provide refined quantitative bounds on the concentration of the transform. These results contribute to a deeper understanding of the localization properties of the QPDHT and extend classical uncertainty principles to a broader analytical framework.