Linear independence of pseudo-splines

Bin Dong, Zuowei Shen

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

In this paper, we show that the shifts of a pseudo-spline are linearly independent. This is stronger than the (more obvious) statement that the shifts of a pseudo-spline form a Riesz system. In fact, the linear independence of a compactly supported (refinable) function and its shifts has been studied in several areas of approximation and wavelet theory. Furthermore, the linear independence of the shifts of a pseudo-spline is a necessary and sufficient condition for the existence of a compactly supported function whose shifts form a biorthogonal dual system of the shifts of the pseudo-spline.

Original languageEnglish (US)
Pages (from-to)2685-2694
Number of pages10
JournalProceedings of the American Mathematical Society
Volume134
Issue number9
DOIs
StatePublished - Sep 1 2006

Keywords

  • Linear independence
  • Pseudo-spline
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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