Approximation by periodic multivariate quasi-projection operators

Abstract

Approximation properties of quasi-projection operators Qj(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.