Uniform approximation by multivariate quasi-projection operators

Abstract

AbstractApproximation properties of quasi-projection operators $$Q_j(f,\varphi , \widetilde{\varphi })$$ Q j ( f , φ , φ ~ ) are studied. These operators are associated with a function $$\varphi $$ φ satisfying the Strang–Fix conditions and a tempered distribution $$\widetilde{\varphi }$$ φ ~ such that compatibility conditions with $$\varphi $$ 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-type spaces. Under additional assumptions on $$\varphi $$ φ and $$\widetilde{\varphi }$$ φ ~ , two-sided estimates in terms of realizations of the K-functional are also established.