On the coefficients of starlike functions

Abstract

Abstract.Every probability measure p on the circle group generates a function / that is starlike univalent on the open unit disc A. In this note the relationship between (cn), the FourierStieltjes coefficients of ¡i, and (an), the Taylor coefficients of/, is examined. A number of theroems are presented which indicate (possibly in the presence of fairly mild restrictions) that the sequences (cn) and (nan) behave similarly. For example, it is shown that if/(A) is finite, then (c") converges to zero if, and only if, (nan) converges to zero, thereby completing a result of Pommerenke.