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Estimates of Approximating Characteristics and the Properties of the Operators of Best Approximation for the Classes of Periodic Functions in the Space B1,1

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Ukrainian Mathematical Journal Aims and scope

We obtain the exact-order estimates for the orthoprojection widths and similar approximating characteristics of the Sobolev classes \( {W}_{p,\alpha}^r \) and Nikol’skii–Besov classes \( {B}_{p,\theta}^r \) of periodic functions of one and several variables in the norm of the space B1,1. In addition, it is established that the sequence of norms of linear operators realizing the orders of the best approximations for the classes \( {B}_{1,\theta}^r \) in the space B1,1 with the help of trigonometric polynomials with “numbers” of harmonics from step hyperbolic crosses is unbounded in the many-dimensional case.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. S. Romanyuk & S. Ya. Yanchenko

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  1. A. S. Romanyuk
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  2. S. Ya. Yanchenko
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Correspondence to S. Ya. Yanchenko.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 8, pp. 1102–1119, August, 2021. Ukrainian DOI: 10.37863/ umzh.v73i8.6755.

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Romanyuk, A.S., Yanchenko, S.Y. Estimates of Approximating Characteristics and the Properties of the Operators of Best Approximation for the Classes of Periodic Functions in the Space B1,1. Ukr Math J 73, 1278–1298 (2022). https://doi.org/10.1007/s11253-022-01990-x

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  • DOI: https://doi.org/10.1007/s11253-022-01990-x

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