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Approximation of \(\bar \omega \)-integrals of continuous functions defined on the real axis by Fourier operators

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Abstract

We obtain asymptotic formulas for the deviations of Fourier operators on the classes of continuous functions \(\hat C_\infty ^{\bar \psi } \) and \(\hat C^{\bar \psi } H_\omega \) in the uniform metric. We also establish asymptotic laws of decrease of functionals characterizing the problem of the simultaneous approximation of \({\bar \psi }\)-integrals of continuous functions by Fourier operators in the uniform metric.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 663–676, May, 2004.

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Sokolenko, I.V. Approximation of \(\bar \omega \)-integrals of continuous functions defined on the real axis by Fourier operators. Ukr Math J 56, 799–816 (2004). https://doi.org/10.1007/s11253-005-0096-8

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Keywords

  • Continuous Function
  • Real Axis
  • Asymptotic Formula
  • Simultaneous Approximation
  • Fourier Operator