Uniform approximation by multivariate quasi-projection operators

08/16/2020

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by   Yurii Kolomoitsev, et al.

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Approximation properties of quasi-projection operators Q_j(f,φ, φ) are studied. Such an operator is associated with a function φ satisfying the Strang-Fix conditions and a tempered distribution φ such that compatibility conditions with φ hold. Error estimates in the uniform norm are obtained for a wide class of quasi-projection operators defined on the space of uniformly continuous functions and on the anisotropic Besov spaces. Under additional assumptions on φ and φ, two-sided estimates in terms of realizations of the K-functional are also obtained.