Power series of Bernstein operators and approximation of resolvents (Q1762369)

According to the theory developed by Altomare et al., certain \(C_0\)-semigroups can be approximated by iterates of positive linear operators. \textit{A. Albanese} et al. [J. Appl. Funct. Anal. 1, No. 3, 343--358 (2006; Zbl 1099.41017)] proved that the resolvent \((\lambda - A)^{-1}\) of the infinitesimal generator of such a semigroup can be also approximated for \(\lambda > 0\) by suitable iterates. Here, the author gives an answer in the case where the semigroup is approximated by the classical Bernstein operators \(B_n\) on the canonical simplex \(S\) of \(\mathbb{R}^d \).