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Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables

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Ukrainian Mathematical Journal Aims and scope

We establish order estimates for the entropy numbers of the Nikol’skii–Besov classes B r p,θ of periodic functions of many variables in the space L q with certain relations between the parameters p and q. By using the obtained lower estimates of the entropy numbers, we establish the exact-order estimates for the Kolmogorov widths of the same classes of functions in the space L 1.

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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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 11, pp. 1540–1556, November, 2015.

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Romanyuk, A.S. Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables. Ukr Math J 67, 1739–1757 (2016). https://doi.org/10.1007/s11253-016-1186-5

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  • DOI: https://doi.org/10.1007/s11253-016-1186-5

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