Abstract
The aim of this paper is to prove an uncertainty principle for the basic Bessel transform of order alpha >= -1/2. In order to obtain a sharp uncertainty principle, we introduce and study a generalized q-Bessel-Dunkl transform which is based on the q-eigenfunctions of the q-Dunkl operator newly given by:
T(alpha,q)(f)(x) = D(q)f(x) + [2 alpha + 1](q)/2q(2 alpha+1) f(x) - f(-x)/x.
In this work, we will follow the same steps of Fitouhi et al. (Math. Sci. Res. J., 2007) using the operator T(alpha,q) instead of the q-derivative.