Power series of Beta operators

摘要

In this paper we investigate the power series of Beta operators. We first study the convergence of this series and describe the Voronovskaya operator A and the inverse Voronovskaya operator. Then, a quantitative convergence result for the inverse Voronovskaya operator via smoothing approach is given. The power series is also related to the resolvent of A and the semigroup generated by A.