@inbook{d72a94ad54574e7cbee5facfac082469,
title = "On de Boor–Fix Type Functionals for Minimal Splines",
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.",
keywords = "Approximation functional, B-spline, Biorthogonal system, de Boor–Fix functional, Dual functional, Minimal spline, Nonpolynomial spline",
author = "Kulikov, {Egor K.} and Makarov, {Anton A.}",
note = "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. Birkh{\"a}user, Cham",
year = "2019",
month = nov,
day = "20",
doi = "10.1007/978-3-030-12277-5_13",
language = "English",
isbn = "9783030122768",
series = "Applied and Numerical Harmonic Analysis",
publisher = "Springer Nature",
pages = "211--225",
editor = "M. Abell and E. Iacob and A. Stokolos and S. Taylor and S. Tikhonov and J. Zhu",
booktitle = "Topics in Classical and Modern Analysis",
address = "Germany",
}