Approximation of functions with a bounded mixed difference by trigonometric polynomials, and the widths of some classes of functions

This paper investigates the approximation of periodic functions of several variables by trigonometric polynomials whose harmonics lie in hyperbolic crosses. It is shown that in many cases the order of the widths, in the sense of Kolmogorov, can be found for classes of functions with a bounded mixed derivative or difference. The possibilities of linear methods of approximation are investigated.
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