Quasi-greedy systems of integer translates

Morten Nielsen; Hrvoje Sikic

Quasi-greedy systems of integer translates

Institut for Matematiske Fag

Publikation: Bog/antologi/afhandling/rapport › Rapport › Forskning

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 basis of integer translates in a finitely generated shift invariant space.

Originalsprog	Engelsk

Forlag	Department of Mathematical Sciences, Aalborg University
Antal sider	10
Status	Udgivet - 2007

Navn	Research Report Series
Nummer	R-2007-30
ISSN	1399-2503

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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 basis of integer translates in a finitely generated shift invariant space.",

author = "Morten Nielsen and Hrvoje Sikic",

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T1 - Quasi-greedy systems of integer translates

AU - Nielsen, Morten

AU - Sikic, Hrvoje

PY - 2007

Y1 - 2007

N2 - 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 basis of integer translates in a finitely generated shift invariant space.

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 basis of integer translates in a finitely generated shift invariant space.

Quasi-greedy systems of integer translates

Abstract

AUB Link

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Citationsformater