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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