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arXiv · 2008.06977

Uniform approximation by multivariate quasi-projection operators

Yurii Kolomoitsev·Maria Skopina
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Abstract

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

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Yurii Kolomoitsev, Maria Skopina. 2020-08-16. Uniform approximation by multivariate quasi-projection operators. https://arxiv.org/abs/2008.06977

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