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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 10, Pages 1756–1767 (Mi zvmmf9761)  
Schoenberg’s polynomial B-splines of odd degrees: A brief review of application

V. G. Alekseev, V. A. Sukhodoev

Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia
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Abstract: A brief overview of applications of Schoenberg’s polynomial B-splines of odd degrees in mathematical statistics, computational mathematics, and statistical radio engineering is provided. Exact formulas for the found Schoenberg B-spline of 15th degree are presented. High-quality approximations of smooth functions with an infinite Fourier transform by functions with a finite Fourier transform are found.
Key words: Schoenberg's B-splines of odd degrees, admissible estimates of probability density, spectral density estimate, analog linear filters, approximation of functions, summation of series.
Received: 14.03.2012
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 10, Pages 1331–1341
DOI: https://doi.org/10.1134/S096554251
Bibliographic databases:
Document Type: Article
UDC: 519.652.3
Language: Russian
Citation: V. G. Alekseev, V. A. Sukhodoev, “Schoenberg’s polynomial B-splines of odd degrees: A brief review of application”, Zh. Vychisl. Mat. Mat. Fiz., 52:10 (2012), 1756–1767; Comput. Math. Math. Phys., 52:10 (2012), 1331–1341
Citation in format AMSBIB
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\by V.~G.~Alekseev, V.~A.~Sukhodoev
\paper Schoenberg’s polynomial B-splines of odd degrees: A brief review of application
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2012
\vol 52
\issue 10
\pages 1756--1767
\mathnet{http://mi.mathnet.ru/zvmmf9761}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3150291}
\zmath{https://zbmath.org/?q=an:1274.65018}
\transl
\jour Comput. Math. Math. Phys.
\yr 2012
\vol 52
\issue 10
\pages 1331--1341
\crossref{https://doi.org/10.1134/S096554251}
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    		Æóðíàë âû÷èñëèòåëüíîé ìàòåìàòèêè è ìàòåìàòè÷åñêîé ôèçèêè Computational Mathematics and Mathematical Physics
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