Multivariate approximation by modified Gauss-Weierstrass operators

摘要

We consider a generalization (Gn)n of the classical sequence of Gauss-Weierstrass operators, in order to obtain a Voronovskaja-type formula involving the general differential operator. These operators have nice approximation, regularity and shape-preserving properties. In particular, by means of Gn and its powers, we characterize the domains of all the realizations of A generating a positive C0-semigroup and we approximate such semigroup. We also discuss some qualitative properties of the semigroup as positivity, convexity and regularity preservation.