Quasi-greedy systems of integer translates

Morten Nielsen; Hrvoje Sikic

doi:10.1016/j.jat.2008.04.009

Quasi-greedy systems of integer translates

Morten Nielsen, Hrvoje Sikic

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

7 Citationer (Scopus)

Abstract

We consider quasi-greedy systems of integer translates in a finitely generated shift-invariant subspace of L₂(R^d), 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.
Udgivelsesdato: NOV

Originalsprog	Engelsk
Tidsskrift	Journal of Approximation Theory
Vol/bind	155
Udgave nummer	1
Sider (fra-til)	43-51
Antal sider	9
ISSN	0021-9045
DOI	https://doi.org/10.1016/j.jat.2008.04.009
Status	Udgivet - 2008

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10.1016/j.jat.2008.04.009

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abstract = "We consider quasi-greedy systems of integer translates in a finitely generated shift-invariant subspace of L2(Rd), 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.",

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AU - Sikic, Hrvoje

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AB - We consider quasi-greedy systems of integer translates in a finitely generated shift-invariant subspace of L2(Rd), 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.

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DO - 10.1016/j.jat.2008.04.009

M3 - Journal article

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VL - 155

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JO - Journal of Approximation Theory

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Quasi-greedy systems of integer translates

Abstract

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