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Approximation by multivariate quasi-projection operators and Fourier multipliers (2006.13272v2)
Published 23 Jun 2020 in math.CA, cs.NA, and math.NA
Abstract: Multivariate quasi-projection operators $Q_j(f,\varphi, \widetilde{\varphi})$, associated with a function $\varphi$ and a distribution/function $\widetilde{\varphi}$, are considered. The function $\varphi$ is supposed to satisfy the Strang-Fix conditions and a compatibility condition with $\widetilde{\varphi}$. 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 $1\le p\le \infty$. In particular, upper and lower estimates of the $L_p$-error of approximation in terms of moduli of smoothness and best approximations are obtained.