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Ukrainian Mathematical Journal

, Volume 67, Issue 6, pp 815–837 | Cite as

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

  • V. V. Bodenchuk
  • A. S. Serdyuk
Article
  • 25 Downloads
We prove that the kernels of analytic functions of the form
$$ {H}_{h,\beta }(t)={\displaystyle \sum_{k=1}^{\infty}\frac{1}{ \cosh kh} \cos \left(kt-\frac{\beta \pi }{2}\right),}h>0,\beta \in \mathbb{R}, $$
satisfy Kushpel’s condition C y,2n starting from a certain number n h explicitly expressed via the parameter h of smoothness of the kernel. As a result, for all n ≥ n h , we establish lower bounds for the Kolmogorov widths d 2n in the space C of functional classes that can be represented in the form of convolutions of the kernel H h,β with functions φ⊥1 from the unit ball in the space L .

Keywords

Analytic Function Periodic Function Approximation Theory Ukrainian National Academy Poisson Integral 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. V. Bodenchuk
    • 1
  • A. S. Serdyuk
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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