Quasi-greedy systems of integer translates

Abstract

We consider quasi-greedy systems of integer translates in a finitely generated shift-invariant subspace of $L_2\left({\mathbb{R}}^d\right)$, that is systems for which the thresholding approximation procedure is well behaved. We prove that every quasi-greedy system of integer translates is also a Riesz basis for its closed linear span. The result shows that there are no conditional quasi-greedy bases of integer translates in a finitely generated shift-invariant space.