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.