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Dal'nevostochnyi Matematicheskii Zhurnal, 2019, Volume 19, Number 1, Pages 10–19 (Mi dvmg391)  

This article is cited in 2 scientific papers (total in 2 papers)

Extremal cubature formulas for anisotropic classes

V. A. Bykovskii

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
Full-text PDF (530 kB) Citations (2)
References:
Abstract: Let E(α;s) be a class of periodical functions
f(x1,,xs)=(m1,,ms)Zsc(m1,,ms)exp(2πi(m1x1++msxs))
with |c(m1,,ms)|j=1(max(1,|mj|))α, and 1<α<. In this work for all natural numbers 1<N< we prove best possible estimation
RN(E(α;s))α,s(logN)s1Nα
for the error of the best cubature formula on the class E(α;s) with N nodes and weights. Similar results are proved for other classes of functions.
Key words: cubature formulas, anisotropic classes of functions.
Received: 21.05.2019
Document Type: Article
UDC: 519.68
MSC: 65J01
Language: Russian
Citation: V. A. Bykovskii, “Extremal cubature formulas for anisotropic classes”, Dal'nevost. Mat. Zh., 19:1 (2019), 10–19
Citation in format AMSBIB
\Bibitem{Byk19}
\by V.~A.~Bykovskii
\paper Extremal cubature formulas for anisotropic classes
\jour Dal'nevost. Mat. Zh.
\yr 2019
\vol 19
\issue 1
\pages 10--19
\mathnet{http://mi.mathnet.ru/dvmg391}
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  • https://www.mathnet.ru/eng/dvmg/v19/i1/p10
  • This publication is cited in the following 2 articles:
    1. Sh. A. Balgimbayeva, D. B. Bazarkhanov, “Optimal cubature formulas for Morrey type function classes on multidimensional torus”, Eurasian Math. J., 15:3 (2024), 25–37  mathnet  crossref
    2. D. B. Bazarkhanov, “Optimal Cubature Formulas on Classes of Periodic Functions in Several Variables”, Proc. Steklov Inst. Math., 312 (2021), 16–36  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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