Best approximations of the classes B p, r of periodic functions of many variables in uniform metric

Author： Romanyuk A.  

Publisher： Springer Publishing Company

ISSN： 0041-5995

Source： Ukrainian Mathematical Journal, Vol.58, Iss.10, 2006-10, pp. : 1582-1596

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Abstract

We obtain estimates exact in order for the best approximations of the classes B ∞, r of periodic functions of two variables in the metric of L ∞ by trigonometric polynomials whose spectrum belongs to a hyperbolic cross. We also investigate the best approximations of the classes B p, r , 1 ≤ p < ∞,="" of="" periodic="" functions="" of="" many="" variables="" in="" the="" metric="" of="">L ∞ by trigonometric polynomials whose spectrum belongs to a graded hyperbolic cross.

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