Dynamical sampling for shift-preserving operators

AGUILERA, A.; CABRELLI, C.; CARBAJAL, D.; PATERNOSTRO, V.

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2021 vol. 51 p. 258 - 274

1063-5203

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.