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On the best approximations and Kolmogorov widths of besov classes of periodic functions of many variables

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Abstract

Order estimates are obtained for the best approximations of the classesB 1, θ r in the spaceL q with 1<q<∞ and classesB ∞, θ r in a uniform metric. The behavior of Kolmogorov widths of the classesB p, θ r ,1<p≤∞, in the metric of L is studied.

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 79–92, January, 1995.

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Romanyuk, A.S. On the best approximations and Kolmogorov widths of besov classes of periodic functions of many variables. Ukr Math J 47, 91–106 (1995). https://doi.org/10.1007/BF01058799

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Keywords

  • Periodic Function
  • Order Estimate
  • Kolmogorov Width
  • Besov Class