Approximation by multivariate quasi-projection operators and Fourier multipliers

06/23/2020

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by   Yurii Kolomoitsev, et al.

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Multivariate quasi-projection operators Q_j(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 studied approximation properties of such operators for functions f from anisotropic Besov spaces and L_p spaces with 1< p<∞. In particular, upper and lower estimates of the L_p-error of approximation in terms of moduli of smoothness and best approximations are obtained.