Some applications of Cartan's theorem to normality and semiduality of gap power series

In this paper we give partial solutions to some questions concerning analytic functions with AP-Gaps raised by Pinto, Ruscheweyh and Salinas (cf. 9], 12]) using a theorem of H. Cartan which extends Montel's theorem on analytic functions omitting the values 0 and 1. Using the same method, we also prove a generalization of a theorem in 9] on the dual hull of sets containing two elements.