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Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths

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Abstract

We obtain estimates of the best polynomial approximations, uniform in the closure B of Faber domains of the complex plane ℂ, for functions continuous in B and defined by Cauchy-type integrals with densities possessing certain generalized differential properties. We establish estimates exact in order for the Kolmogorov widths of classes of such functions in relevant functional spaces.

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Authors
  1. V. S. Romanyuk
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Romanyuk, V.S. Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths. Ukr Math J 48, 267–282 (1996). https://doi.org/10.1007/BF02372051

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  • DOI: https://doi.org/10.1007/BF02372051

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