Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torresani Uncertainty Principle

Let \ₙ\₍=₁^ and \ₘ\₌=₁^ be two modular Parseval frames for a Hilbert C*-module E. Then for every x E\0\, we show that alignUE \|_ x \|₀ \|_ x \|₀ 1₍, ₌ ₍ \| ₙ, ₘ \|². align We call Inequality (UE) as Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'esani Uncertainty Principle. Inequality (UE) is the noncommutative analogue of breakthrough Ricaud-Torr\'esani uncertainty principle IEEE Trans. Inform. Theory, 2013. In particular, Inequality (UE) extends Elad-Bruckstein uncertainty principle IEEE Trans. Inform. Theory, 2002 and Donoho-Stark uncertainty principle SIAM J. Appl. Math. , 1989.