On de Boor–Fix Type Functionals for Minimal Splines

  • Egor K. Kulikov
  • Anton A. MakarovEmail author
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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.


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



The reported study was funded by a grant of the President of the Russian Federation (MD-2242.2019.9).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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