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

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

7 Citations (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.

Original language	English
Journal	Journal of Approximation Theory
Volume	155
Issue number	1
Pages (from-to)	43-51
Number of pages	9
ISSN	0021-9045
DOIs	https://doi.org/10.1016/j.jat.2008.04.009
Publication status	Published - 2008

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title = "Quasi-greedy systems of integer translates",

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.

U2 - 10.1016/j.jat.2008.04.009

DO - 10.1016/j.jat.2008.04.009

M3 - Journal article

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VL - 155

SP - 43

EP - 51

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

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ER -

Quasi-greedy systems of integer translates

Abstract

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