Approximation by multivariate quasi-projection operators and Fourier multipliers

Yurii Kolomoitsev and Maria Skopina

Applied Mathematics and Computation, 2021, vol. 400, issue C

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.

Keywords: Quasi-projection operator; Besov space; Error estimate; Anisotropic best approximation; Anisotropic moduli of smoothness; Fourier multipliers (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000035

DOI: 10.1016/j.amc.2021.125955

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