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Approximation of functions of several variables on a torus by trigonometric polynomials. (Russian) Zbl 0634.42005
The paper deals with the approximation problem of periodical functions of several variables, smoothness of which is given by generalized modulus of continuity. It is studied the best approximation problem by Fourier sums, the Fourier diameters and Kolmogorov diameters and it is also considered the estimates problem for some integrals and sums on convex sets or on their complements. The author generalizes his own earlier results [Constructive theory of func. Proc. Int. Conf., Varna/Bulg. 1984, 43–48 (1984; Zbl 0609.42003) and Usp. Mat. Nauk 34, No. 4(208), 189–190 (1979; Zbl 0435.41009), ibid. 38, No. 6, 111–112 (1983; Zbl 0541.42010), Mat. Zametki 36, No. 4, 479–492 (1984; Zbl 0589.42013)]. The main theorems and the auxiliary results used in the proofs are too complicated to be stated here.

42A10 Trigonometric approximation
42A05 Trigonometric polynomials, inequalities, extremal problems
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