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Kolmogorov Widths and Bilinear Approximations of the Classes of Periodic Functions of One and Many Variables

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Ukrainian Mathematical Journal Aims and scope

We obtain the exact order estimates for the Kolmogorov widths of the classes \( {W}_p^g \) of periodic functions of one variable generated by the integral operators with kernels g(x, y) from the Nikol’skii–Besov classes \( {B}_{\mathrm{p},\theta}^{\mathrm{r}} \). We also study the behaviors of bilinear approximations to the classes \( {W}_{\mathrm{p},\alpha}^{\mathrm{r}} \)of periodic multivariate functions with bounded mixed derivative in the spaces Lq1,q2 for some relations between the parameters r1, p, q1, and q2.

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Authors and Affiliations

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

    A. S. Romanyuk

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  1. A. S. Romanyuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 2, pp. 224–235, February, 2018.

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Romanyuk, A.S. Kolmogorov Widths and Bilinear Approximations of the Classes of Periodic Functions of One and Many Variables. Ukr Math J 70, 252–265 (2018). https://doi.org/10.1007/s11253-018-1499-7

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  • DOI: https://doi.org/10.1007/s11253-018-1499-7

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