Quasi-greedy systems of integer translates

  • Authors:

  • Morten Nielsen;Hrvoje Šikić

  • Affiliations:

  • Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK - 9220 Aalborg East, Denmark;Department of Mathematics, University of Zagreb, Bijenička 30, HR-10000, Zagreb, Croatia

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2008

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Abstract

We consider quasi-greedy systems of integer translates in a finitely generated shift-invariant subspace of L"2(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.