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Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions

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Abstract

Lower estimates of the Kolmogorov widths are obtained for certain classes of infinitely differentiable periodic functions in the metrics of C and L. For many important cases, these estimates coincide with the values of the best approximations of convolution classes by trigonometric polynomials calculated by Nagy, and, hence, they are exact.

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References

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Authors
  1. A. S. Serdyuk
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1700–1706, December, 1997.

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Serdyuk, A.S. Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions. Ukr Math J 49, 1919–1926 (1997). https://doi.org/10.1007/BF02513071

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  • DOI: https://doi.org/10.1007/BF02513071

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