Donoho–Stark and Price uncertainty principles for a class of q-integral transforms with bounded kernels

Abstract

We consider a very global q-integral transform, essentially characterized by having a bounded kernel and satisfying a set of natural and useful properties for the realization of applications. The main ambition of this work is to seek conditions that guarantee uncertainty principles of the Donoho–Stark type for that class of q-integral transforms. It should be noted that the global character of the q-integral transform in question allows one to immediately deduce corresponding Donoho–Stark uncertainty principles for q-integral operators that are its particular cases. These particular cases are very well-known operators, namely: a q-cosine-Fourier transform, a q-sine-Fourier transform, a q-Fourier transform, a q-Bessel–Fourier transform and a q-Dunkl transform. Moreover, generalizations of the local uncertainty principle of Price for the q-cosine-Fourier transform, q-sine-Fourier transform, q-Fourier transform, q-Bessel–Fourier transform and q-Dunkl transform are also obtained.