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Estimates of the best orthogonal trigonometric approximations and orthoprojective widths of the classes of periodic functions of many variables in a uniform metric

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Abstract

Some approximative characteristics of classes of periodic functions of many variables \( {L}_{\beta, p}^{\psi }, \) 1 < p < 1, in a uniform metric are investigated. The first part of the paper is devoted to the construction of estimates of the best orthogonal trigonometric approximations of the mentioned classes in the space L∞. In the second part, we have established the ordinal estimates of the orthoprojective widths of the classes \( {L}_{\beta, p}^{\psi }, \) 1 < p < 1, in the same space, as well as the estimates of another approximative characteristic which is close, in a definite meaning, to the orthoprojective width.

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Authors and Affiliations

  1. State University of Telecommunications, Kyiv, Ukraine

    Hanna M. Vlasyk, Viktoriya V. Shkapa & Iryna V. Zamrii

Authors
  1. Hanna M. Vlasyk
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  2. Viktoriya V. Shkapa
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  3. Iryna V. Zamrii
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Correspondence to Hanna M. Vlasyk.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 3, pp. 448–460 July–September, 2019.

Translated from Ukrainian by V.V. Kukhtin

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Vlasyk, H.M., Shkapa, V.V. & Zamrii, I.V. Estimates of the best orthogonal trigonometric approximations and orthoprojective widths of the classes of periodic functions of many variables in a uniform metric. J Math Sci 246, 110–119 (2020). https://doi.org/10.1007/s10958-020-04725-0

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