Über gewisse nichtfortsetzbare Potenzreihen. II.
We establish certain properties for the class of universal functions in with respect to the center , for certain types of connected non-simply connected domains . In the case where is discrete we prove that this class is -dense in , depends on the center and that the analog of Kahane’s conjecture does not hold.
2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated....