Uniform approximation by multivariate quasi-projection operators

Abstract

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

arXiv admin note: text overlap with arXiv:2006.13272