On interpolational and extremal properties of periodic perfect splines

Authors

  • V. F. Babenko
  • O.V. Kovalenko

DOI:

https://doi.org/10.15407/dopovidi2014.12.007

Keywords:

interpolational and extremal properties, perfect splines

Abstract

The existence and the extremal property of a periodic perfect spline, which interpolates the given function in mean, are proved.

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References

Korneychuk N. P. Exact constants in approximation theory, Moscow: Nauka, 1987 (in Russian).

Korneychuk N. P., Babenko V. F., Ligun A. A. Extreme properties of polynomials and splines, Kiev: Nauk. Dumka, 1992 (in Russian).

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Karlin S. Trans. Amer. Math. Soc., 1975, 206: 25–66. https://doi.org/10.1090/S0002-9947-1975-0367512-0

Akhiezer N. I. Dokl. AN USSR, 1937, 17 (in Russian).

Akhiezer N. I. Dokl. AN USSR, 1938, 18 (in Russian).

Nikolskiy S. M. Izv. AN USSR. Ser. mathem., 1946, 10, No 3: 207–256 (in Russian).

Mairhuber J. C., Schoenberg I. J., Williamson R. E. Rend. Circ. Mat. Palermo, 1959, 8, No 2: 241–270. https://doi.org/10.1007/BF02843691

Galeev E. M., Tikhomirov V. M. A short course on the theory of extreme problems, Moscow: Izd-vo Mosk. un-ta, 1983 (in Russian).

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Published

19.03.2025

How to Cite

Babenko, V. F., & Kovalenko, O. (2025). On interpolational and extremal properties of periodic perfect splines . Reports of the National Academy of Sciences of Ukraine, (6), 7–11. https://doi.org/10.15407/dopovidi2014.12.007

Issue

No. 6 (2022): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

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