Abstract
In this work, using some elements of the q-harmonic analysis and the q-Dunkl transform, for fixed q is an element of]0, 1[, we establish a q-analogue of uncertainty inequalities for orthonormal sequences and prove a quantitative version of Shapiro's uncertainty principle for the q-Dunkl transform. As a side results, we prove a variation of Donoho-Stark's uncertainty inequality, in particular, if f is is an element of s-concentrated on S and F-D(alpha,q)(f) is is an element of Sigma-concentrated on Sigma with broken vertical bar broken vertical bar f broken vertical bar broken vertical bar 2,q = 1 and is an element of s + is an element of Sigma < 1, then broken vertical bar S broken vertical bar broken vertical bar Sigma broken vertical bar >= (1 - (is an element of s + is an element of Sigma))(2).