On de Boor–Fix Type Functionals for Minimal Splines

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2 Scopus citations


This paper considers minimal coordinate splines. These splines as a special case include well-known polynomial B-splines and share most properties of B-splines (linear independency, smoothness, nonnegativity, etc.). We construct a system of dual functionals biorthogonal to the system of minimal splines. The obtained results are illustrated with an example of a polynomial generating vector function, which leads to the construction of B-splines and the de Boor–Fix functionals. For nonpolynomial generating vector functions we give formulas for the construction of nonpolynomial splines and the dual de Boor–Fix type functionals.

Original languageEnglish
Title of host publicationTopics in Classical and Modern Analysis
EditorsM. Abell, E. Iacob, A. Stokolos, S. Taylor, S. Tikhonov, J. Zhu
Place of PublicationCham
PublisherSpringer Nature
ISBN (Electronic)9783030122775
ISBN (Print)9783030122768
StatePublished - 20 Nov 2019

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Scopus subject areas

  • Applied Mathematics


  • Approximation functional
  • B-spline
  • Biorthogonal system
  • de Boor–Fix functional
  • Dual functional
  • Minimal spline
  • Nonpolynomial spline


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