On Some Inequalities of Uncertainty Principles Type in Quantum Calculus

Abstract

The aim of this paper is to generalize the -Heisenberg uncertainty principles studied by Bettaibi et al. (2007), to state local uncertainty principles for the -Fourier-cosine, the -Fourier-sine, and the -Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the -Bessel-Fourier transform.

A Quantum Wavelet Uncertainty Principle

“…In q-theory, the uncertainty principle has been the subject of several studies, in both Fourier and wavelet frameworks. In [73], the authors developed a general q-Heisenberg uncertainty principle for the q-Fourier-cosine/sine and the q-Bessel-Fourier transform. In [74], a Heisenberg-Weyl type uncertainty principle has been shown for a q-Dunkl transform.…”