Parametric Representation of Infinitesimal Generators on the Polydisk

摘要

In this paper, analogues of the Berkson-Porta formula for the infinitesimal generators of one-parameter semigroup of holomorphic self-maps on the polydisk are obtained. We give a necessary and sufficient condition for a holomorphic vector field to be an infinitesimal generator which improves the theorem given by Contreras, de Fabritiis and Diaz-Madrigal.