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Topics in Classical and Modern Analysis pp 211–225Cite as

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On de Boor–Fix Type Functionals for Minimal Splines

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

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.

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Acknowledgement

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

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    Egor K. Kulikov & Anton A. Makarov

Authors
  1. Egor K. Kulikov
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  2. Anton A. Makarov
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Corresponding author

Correspondence to Anton A. Makarov .

Editor information

Editors and Affiliations

  1. Georgia Southern University, Statesboro, GA, USA

    Martha Abell

  2. Georgia Southern University, Statesboro, GA, USA

    Emil Iacob

  3. Georgia Southern University, Statesboro, GA, USA

    Alex Stokolos

  4. Georgia Southern University, Statesboro, GA, USA

    Sharon Taylor

  5. ICREA, Passeig de Lluís Companys, Barcelona, Spain ; Centre de Recerca Matemàtica, Barcelona, Spain

    Sergey Tikhonov

  6. Georgia Southern University, Statesboro, GA, USA

    Jiehua Zhu

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Kulikov, E.K., Makarov, A.A. (2019). On de Boor–Fix Type Functionals for Minimal Splines. In: Abell, M., Iacob, E., Stokolos, A., Taylor, S., Tikhonov, S., Zhu, J. (eds) Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12277-5_13

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