Refined support and entropic uncertainty inequalities

Benjamin Ricaud; Bruno Torrésani

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arXiv · 1210.7711

Refined support and entropic uncertainty inequalities

Benjamin Ricaud·Bruno Torrésani

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Abstract

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 has been obtained by introducing a generalization of the coherence. In the finite dimensional case and under certain conditions, minimizers of this inequalities are given as constant functions on their support. In addition, $\ell^p$-norms inequalities are introduced as byproducts of the entropic inequalities.

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Benjamin Ricaud, Bruno Torrésani. 2012-10-29. Refined support and entropic uncertainty inequalities. https://arxiv.org/abs/1210.7711

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