Multivariate approximation by modified Gauss-Weierstrass operators

Abstract

We consider a generalization (G n ) n of the classical sequence of Gauss-Weierstrass operators, in order to obtain a Voronovskaja-type formula involving the general differentialThese operators have nice approximation, regularity and shape-preserving properties. In particular, by means of G n and its powers, we characterize the domains of all the realizations of A generating a positive C 0 -semigroup and we approximate such semigroup. We also discuss some qualitative properties of the semigroup as positivity, convexity and regularity preservation.