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Best approximations of the classes B r p,θ of periodic functions of many variables in uniform metric

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Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain estimates exact in order for the best approximations of the classes B r∞,θ of periodic functions of two variables in the metric of L ∞ by trigonometric polynomials whose spectrum belongs to a hyperbolic cross. We also investigate the best approximations of the classes B r p,θ , 1 ≤ p < ∞, of periodic functions of many variables in the metric of L ∞ by trigonometric polynomials whose spectrum belongs to a graded hyperbolic cross.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. S. Romanyuk

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  1. A. S. Romanyuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1395–1406, October, 2006.

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Romanyuk, A.S. Best approximations of the classes B r p,θ of periodic functions of many variables in uniform metric. Ukr Math J 58, 1582–1596 (2006). https://doi.org/10.1007/s11253-006-0155-9

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  • DOI: https://doi.org/10.1007/s11253-006-0155-9

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