2023/04/05 by K. Mahesh Krishna, Krishna, K. Mahesh
Engineering · Mathematics · #42C15 #Advanced Harmonic Analysis Research #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Structural Integrity and Reliability Analysis
paper · pdf · doi:10.48550/arxiv.2304.03324
openalex publication_date 2023/04/05 · openalex created_date 2023/04/11 · openalex updated_date 2026/07/28
Let (\fj\j=1n, \τj\j=1n) and (\gk\k=1m, \ωk\k=1m) be p-Schauder frames for a finite dimensional Banach space X. Then for every x ∈ X∖\0\, we show that (1) ‖θf x‖0^(1)/(p)‖θg x‖0^(1)/(q) ≥ \frac1max1≤ j≤ n, 1≤ k≤ m|fj(ωk)| and ‖θg x‖0^(1)/(p)‖θf x‖0^(1)/(q)≥ \frac1max1≤ j≤ n, 1≤ k≤ m|gk(τj)|. where θf: X \ni x ↦ (fj(x) )j=1n ∈ ℓp([n]); θg: X \ni x ↦ (gk(x) )k=1m ∈ ℓp([m]) and q is the conjugate index of p. We call Inequality (1) as Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani Uncertainty Principle. Inequality (1) improves Ricaud-Torrésani uncertainty principle [IEEE Trans. Inform. Theory, 2013]. In particular, it improves Elad-Bruckstein uncertainty principle [IEEE Trans. Inform. Theory, 2002] and Donoho-Stark uncertainty principle [SIAM J. Appl. Math., 1989].