2019/12/21 by Alejandra Aguilera, Carlos Cabrelli, Aguilera, A. +5 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1912.10348
openalex publication_date 2019/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we solve the dynamical sampling problem for a class of shift-preserving operators L:V→ V acting on a finitely generated shift-invariant space V. We find conditions on L and a finite set of functions of V so that the iterations of the operator L on the functions produce a frame generator set of V. This means that the integer translations of the generators form a frame of V.