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Approximation by multivariate quasi-projection operators and Fourier multipliers

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  • Kolomoitsev, Yurii
  • Skopina, Maria

Abstract

Multivariate quasi-projection operators Qj(f,φ,φ˜), associated with a function φ and a distribution/function φ˜, are considered. The function φ is supposed to satisfy the Strang-Fix conditions and a compatibility condition with φ˜. Using technique based on the Fourier multipliers, we study approximation properties of such operators for functions f from anisotropic Besov spaces and Lp spaces with 1≤p≤∞. In particular, upper and lower estimates of the Lp-error of approximation in terms of anisotropic moduli of smoothness and anisotropic best approximations are obtained.

Suggested Citation

  • Kolomoitsev, Yurii & Skopina, Maria, 2021. "Approximation by multivariate quasi-projection operators and Fourier multipliers," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000035
    DOI: 10.1016/j.amc.2021.125955
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    References listed on IDEAS

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    1. Costarelli, D. & Krivoshein, A. & Skopina, M. & Vinti, G., 2019. "Quasi-projection operators with applications to differential-difference expansions," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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