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On optimization of approximate integration over \(d\)-dimensional ball. (English) Zbl 1111.41021
Summary: For classes of functions defined on a ball in \(\mathbb{R}^d\), \(d> 1\), with a given majorant for their moduli of continuity, we obtain an optimal cubature formula which uses \(n\) mean values of the integrand, taken over \((d- 1)\)-dimensional spheres.

MSC:
41A50 Best approximation, Chebyshev systems
41A30 Approximation by other special function classes
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