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Mat. Sb., 2003, Volume 194, Number 10, Pages 133–160 (Mi msb777)  

This article is cited in 3 scientific papers (total in 3 papers)

Quadrature formulae for classes of functions of low smoothness

E. D. Nursultanova, N. T. Tleukhanovab

a Kazakhstan Branch of Lomonosov Moscow State University
b L. N. Gumilev Eurasian National University

Abstract: For Sobolev and Korobov spaces of functions of several variables a quadrature formula with explicitly defined coefficients and nodes is constructed. This formula is precise for trigonometric polynomials with harmonics from the corresponding step hyperbolic cross. The error of the quadrature formula in the classes $W^\alpha_p[0,1]^n$, $E^\alpha[0,1]^n$ is $o((\ln M)^\beta/M^\alpha)$, where $M$ is the number of nodes and $\beta$ is a parameter depending on the class.
The problem of the approximate calculation of multiple integrals for functions in $W^\alpha_p[0,1]^n$ is considered in the case when this class does not lie in the space of continuous functions, that is, for $\alpha\leqslant 1/p$.

DOI: https://doi.org/10.4213/sm777

Full text: PDF file (398 kB)
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English version:
Sbornik: Mathematics, 2003, 194:10, 1559–1584

Bibliographic databases:

UDC: 517.5
MSC: 65D32, 41A55
Received: 11.02.2002 and 12.05.2003

Citation: E. D. Nursultanov, N. T. Tleukhanova, “Quadrature formulae for classes of functions of low smoothness”, Mat. Sb., 194:10 (2003), 133–160; Sb. Math., 194:10 (2003), 1559–1584

Citation in format AMSBIB
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\paper Quadrature formulae for classes of functions of low smoothness
\jour Mat. Sb.
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\issue 10
\pages 133--160
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\transl
\jour Sb. Math.
\yr 2003
\vol 194
\issue 10
\pages 1559--1584
\crossref{https://doi.org/10.1070/SM2003v194n10ABEH000777}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “An application of tensor products of functionals in problems of numerical integration”, Izv. Math., 73:2 (2009), 393–434  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. E. S. Smailov, N. T. Tleukhanova, “Estimation of error of cubature formula in Besov space”, Eurasian Math. J., 1:1 (2010), 147–156  mathnet  mathscinet  zmath
    3. E. D. Nursultanov, N. T. Tleukhanova, “On reconstruction of multiplicative transformations of functions in anisotropic spaces”, Siberian Math. J., 55:3 (2014), 482–497  mathnet  crossref  mathscinet  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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