Resumen de Asymptotic formulae for positive linear operators: direct and converse results

Francesco Altomare, Sabrina Diomede

• This paper is concerned with asymptotic formulae for sequences of positive linear operators acting on weighted spaces of continuous functions defined on a real interval. The main result provides a characterization of those continuous functions for which a pointwise asymptotic formula holds true. The method is essentially based on a characterization of the domains of generators of C0-semigroups in terms of asymptotic formulae. Finally, several applications concerning, among others, Kantorovich operators, exponential operators, Gauss-Weierstrass operators and a sequence of operators related to the Black-Scholes equation are discussed as well.