2024/06/01 by Krishna, K. Mahesh
#42C15 #46L08 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2406.08504
Let \τn\n=1^∞ and \ωm\m=1^∞ be two modular Parseval frames for a Hilbert C*-module E. Then for every x ∈ E∖\0\, we show that (1) ‖θτx ‖0 ‖θωx ‖0 ≥ \frac1supn, m ∈ ℕ ‖⟨ τn, ωm⟩ ‖2. We call Inequality (1) as Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani Uncertainty Principle. Inequality (1) is the noncommutative analogue of breakthrough Ricaud-Torrésani uncertainty principle [IEEE Trans. Inform. Theory, 2013]. In particular, Inequality (1) extends Elad-Bruckstein uncertainty principle [IEEE Trans. Inform. Theory, 2002] and Donoho-Stark uncertainty principle [SIAM J. Appl. Math., 1989].