Dynamical sampling for shift-preserving operators
2021
Abstract 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.
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