Cristian Tacelli

Full length article: On the interpolation of discontinuous functions

Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out to be useful for a detailed description of some phenomena in interpolation theory at points of discontinuity of the first kind. In particular we give some applications to Lagrange operators on Chebyshev nodes of the first and the second kind and Shepard operators.

Trotter's approximation of semigroups and order of convergence in C2,α-spaces

We improve the quantitative estimate of the convergence in Trotters approximation theorem and obtain a representation of the resolvent operators in terms of iterates of linear operators on its whole domain. In the context of the standard simplex we give some estimates for functions of class C^2^,^@a which considerably improve some previous estimates and allow one to establish a partial inverse result.

On the order of convergence of Voronovskaja-type formulas

In this work general quantitative estimates of Voronovskaja-type formulas in the space of functions of several variables that are twice continuously differentiable and in the space of functions with weighted second-order derivatives are established.