Quantitative uncertainty principles associated with the k$$ k $$‐Hankel wavelet transform on ℝd$$ {\mathbb{R}}^d $$

Abstract

The ‐Hankel wavelet transform ( ‐HWT) is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of time‐frequency signal analysis within a short span of time. Knowing the fact that the study of uncertainty principles is both theoretically interesting and practically useful, we formulate several qualitative uncertainty principles for the ‐Hankel wavelet transform. First, we formulate the Heisenberg's uncertainty principle governing the simultaneous localization of a signal and the corresponding ‐HWT via three approaches: ‐type, ‐type, and ‐entropy based. Second, we derive some weighted uncertainty inequalities such as the Pitt's and Beckner's uncertainty inequalities for the ‐HWT. We culminate our study by formulating several concentration‐based uncertainty principles, including the Amrein–Berthier–Benedicks's and local inequalities for the ‐Hankel wavelet transform.