Frames via Unilateral Iterations of a Bounded Operator

2022/01/24 by Victor Bailey, Bailey, Victor · 1 citation
Engineering · #46C99 #47A99 #FOS: Mathematics #Functional Analysis (math.FA) #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2201.09757

openalex publication_date 2022/01/24 · openalex created_date 2022/03/02 · openalex updated_date 2026/07/28

Abstract

Motivated by recent work in Dynamical Sampling, we prove a necessary and sufficient condition for a frame in a separable and infinite-dimensional Hilbert space to admit the form \Tⁿ φ\_{n ≥ 0} with T ∈ B(H). Also, a characterization of all the vectors φ for which \Tⁿ φ\_{n ≥ 0} is a frame for some T ∈ B(H) is provided. Some auxiliary results on operator representations of Riesz frames are given as well.

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