Ukrainian Mathematical Journal

, Volume 67, Issue 8, pp 1137–1145 | Cite as

Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. II

  • V. V. Bodenchuk
  • A. S. Serdyuk
Article

It is shown that the lower bounds of the Kolmogorov widths d2n in the space C established in the first part of our work for the function classes that can be represented in the form of convolutions of the kernels \( {H}_{h,\beta }(t)={\displaystyle \sum_{k=1}^{\infty}\frac{1}{ \cosh kh} \cos \left(kt-\frac{\beta \pi }{2}\right),\kern1em h>0,\kern1em \beta \in \mathbb{R},} \) with functions φ ⊥ 1 from the unit ball in the space L coincide (for all nnh) with the best uniform approximations of these classes by trigonometric polynomials whose order does not exceed n − 1. As a result, we obtain the exact values of widths for the indicated classes of convolutions. Moreover, for all nnh, we determine the exact values of the Kolmogorov widths d2n−1 in the space L1 of classes of the convolutions of functions φ ⊥ 1 from the unit ball in the space L1 with the kernel Hh,β.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • V. V. Bodenchuk
    • 1
  • A. S. Serdyuk
    • 1
  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine

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