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Uniform approximation by multivariate quasi-projection operators

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.