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Universal functions on nonsimply connected domains

Antonios D. Melas (2001)

Annales de l’institut Fourier

We establish certain properties for the class 𝒰 ( Ω , ζ 0 ) of universal functions in Ω with respect to the center ζ 0 Ω , for certain types of connected non-simply connected domains Ω . In the case where / Ω is discrete we prove that this class is G δ -dense in H ( Ω ) , depends on the center ζ 0 and that the analog of Kahane’s conjecture does not hold.

Zeros of Sequences of Partial Sums and Overconvergence

Kovacheva, Ralitza K. (2008)

Serdica Mathematical Journal

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....

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