Approximation characteristics of the Nikol'skii-Besov-type classes of periodic functions of several variables in the space $B_{q,1}$

Authors

  • O.V. Fedunyk-Yaremchuk Lesya Ukrainka Volyn National University, 9 Bankova str., 43025, Lutsk, Ukraine https://orcid.org/0000-0002-6223-1782
  • S.B. Hembars'ka Lesya Ukrainka Volyn National University, 9 Bankova str., 43025, Lutsk, Ukraine https://orcid.org/0000-0001-6137-1970
  • I.A. Romanyuk Lesya Ukrainka Volyn National University, 9 Bankova str., 43025, Lutsk, Ukraine https://orcid.org/0009-0005-1323-6682
  • P.V. Zaderei National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 7 Beresteiskyi av., 03056, Kyiv, Ukraine
https://doi.org/10.15330/cmp.16.1.158-173

Keywords:

Nikol'skii-Besov-type class, step hyperbolic Fourier sum, best approximation, widht
Published online: 2024-06-06

Abstract

We obtained the exact order estimates of approximation of periodic functions of several variables from the Nikol'skii-Besov-type classes $B^{\Omega}_{p,\theta}$ by using their step hyperbolic Fourier sums in the space $B_{q,1}$. The norm in this space is stronger than the $L_q$-norm. In the considered situations, approximations by the mentioned Fourier sums realize the orders of the best approximations by polynomials with "numbers" of harmonics from the step hyperbolic cross. We also established the exact order estimates of the Kolmogorov, linear and trigonometric widths of classes $B^{\Omega}_{p,\theta}$ in the space $B_{q,1}$ for certain relations between the parameters $p$ and $q$.

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How to Cite
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Fedunyk-Yaremchuk, O.; Hembars'ka, S.; Romanyuk, I.; Zaderei, P. Approximation Characteristics of the Nikol’skii-Besov-Type Classes of Periodic Functions of Several Variables in the Space $B_{q,1}$. Carpathian Math. Publ. 2024, 16, 158-173.