Uniform approximation by multivariate quasi-projection operators

2020/08/16 by Yurii Kolomoitsev, Kolomoitsev, Yurii, M. Skopina +1
Mathematics · #Mathematical Approximation and Integration #Approximation Theory and Sequence Spaces #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2008.06977

Abstract

Approximation properties of quasi-projection operators Q_j(f,φ, \widetildeφ) are studied. Such an operator is associated with a function φ satisfying the Strang-Fix conditions and a tempered distribution \widetildeφ 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 \widetildeφ, two-sided estimates in terms of realizations of the K-functional are also obtained.

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