# Interpolazione pesata sulla semiretta reale

Vengono considerati processi di interpolazione al fine di approssimare funzioni con dominio \(\mathbb{R}^+\) e con patologie negli estremi dell’intervallo. Dopo aver mostrato alcuni risultati sulla migliore approssimazione, vengono stabilite condizioni necessarie e sufficienti per la convergenza dei predetti processi interpolatori in differenti metriche.

*Weighted interpolation on the real half-line*

*I consider interpolation processes to approximate functions with domain \(\mathbb{R}^+\) and with pathological behavior at the extremes of the interval.*
*After showing some results on the best approximation, I establish necessary and sufficient conditions for the convergence of the aforementioned interpolation processes in different metrics.*

## Giuseppe Mastroianni

Giuseppe Mastroianni is professor emeritus at the University of Basilicata, where he was full professor of numerical analysis for more than twenty-five years.

«[His] research interests lie in approximation theory and numerical analysis (interpolation processes, positive operators, orthogonal polynomials, quadrature rules, numerical treatment of integral equations, weighted polynomial inequalities, Fourier series, etc.). He has published over two hundred remarkable papers in several prestigious mathematical journals and has been invited to deliver lectures to a number of international conferences as well as to give colloquium and seminar talks in several research centers around the world. He has conducted research in collaboration with several mathematicians, and with some of them he has forged a deep and lasting friendship.»

«[S]ince the beginning of his career, Mastroianni has served as an advisor, encouraging and initiating young students to the realm of mathematical research. For this purpose, he has created the group of Numerical Analysis at the University of Basilicata. […] He has passionately guided the research activity of the scientific group in Potenza, investing also a lot of time and energy in order to create an atmosphere of sincere collaboration and friendship among them.»

(From G. V. Milovanović, D. Occorsio, and M. G. Russo, *Giuseppe Mastroianni – A master in interpolation processes*, Publ. Inst. Math. (Beograd) (N.S.) 96 (2014), pp. 1–4.)