ASYMPTOTIC REPRESENTATIONS OF STAR-LIKE FUNCTIONS VIA CONTINUOUS SEMIGROUPS OF HOLOMORPHIC MAPPINGS

Abstract

We first use linearizations of continuous semigroups of holomorphic mappings to study asymptotic representations of star-like /-analytic functions defined on the open unit ball of a J-algebra and then apply these representations to obtain a distortion theorem for such functions. We also consider some aspects of these representations in general Banach spaces.