Refined Support and Entropic Uncertainty Inequalities

Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality is obtained by introducing a generalization of the coherence. In the finite-dimensional case and under certain conditions, minimizers of these inequalities are given. In addition, l(p) norms inequalities are introduced as byproducts of the entropic inequalities.