This article is cited in 7 papers

Quadrature formulae for classes of functions of low smoothness

E. D. Nursultanov^a, N. T. Tleukhanova<sup>b

a</sup> 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 $\alpha\leqslant 1/p$.

UDC: 517.5

MSC: 65D32, 41A55

Received: 11.02.2002 and 12.05.2003

DOI: 10.4213/sm777

 English version: Sbornik: Mathematics, 2003, 194:10, 1559–1584

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