A quantum wavelet uncertainty principle

TL;DR

This paper establishes a new uncertainty principle for the generalized q-Bessel wavelet transform within the q-calculus framework, extending classical concepts with a two-parameter Bessel operator.

Contribution

It introduces a novel uncertainty principle for the q-Bessel wavelet transform, expanding the theoretical understanding in the q-calculus setting.

Findings

Derived a new uncertainty principle for q-Bessel wavelet transform

Extended classical Bessel operator with two parameters

Explored wavelet uncertainty in the q-calculus framework

Abstract

The aim of this paper is to derive a new uncertainty principle for the generalized $q$-Bessel wavelet transform studied earlier in \cite{Rezguietal}. In this paper, an uncertainty principle associated with wavelet transforms in the $q$-calculus framework has been established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is exploited next to explore a wavelet uncertainty principle already in the $q$-calculus framework.