Quasi-greedy systems of integer translates
type: Item
instance of: scholarly article
title: Quasi-greedy systems of integer translates
zbMATH Open document ID: 1157.42011
author: H. Šikić
author: Morten Nielsen
published in: Journal of Approximation Theory
publication date: 2009-02-03T00:00:00Z
review text: The authors study finitely generated shift-invariant subspaces of \(S\subset L_2(\mathbb{R}^d)\) of the form \[ S=\overline{\text{span}\{\varphi(\cdot-k) : \varphi\in \Phi, k\in \mathbb{Z}^d\}}, \] where \(\Phi\) is a finite seet. They show that if this space has a Schauder basis of the form \(\{\psi(\cdot-k) : \psi\in \Psi, k\in \mathbb{Z}^d\}\) that is quasi-greedy (which means that if one chooses the terms in the series expansion in an order so that the absolute values of the coefficients are not increasing, then one gets convergence), then this basis is in fact a Riesz basis.
reviewed by: Gustaf Gripenberg
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 5501957
zbMATH Keywords: quasi-greedy system
zbMATH Keywords: Schauder basis
zbMATH Keywords: integer translates shift-invariant space
MaRDI profile type: Publication
full work available at URL: j.jat.2008.04.009
OpenAlex ID: W2053642775
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DOI: 10.1016/J.JAT.2008.04.009
description: scientific article; zbMATH DE number 5501957