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Dal'nevostochnyi Matematicheskii Zhurnal, 2019, Volume 19, Number 1, Pages 10–19
(Mi dvmg391)
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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
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)s−1Nα
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
Citation:
V. A. Bykovskii, “Extremal cubature formulas for anisotropic classes”, Dal'nevost. Mat. Zh., 19:1 (2019), 10–19
Linking options:
https://www.mathnet.ru/eng/dvmg391 https://www.mathnet.ru/eng/dvmg/v19/i1/p10
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Abstract page: | 354 | Full-text PDF : | 104 | References: | 66 |
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