Zeros and interpolation by universal Taylor series on simply connected domains

By investigating the relation between growth and value distribution A. Melas established a qualitative version of a Picard type theorem for universal Taylor series, that is: every universal Taylor series on the open unit disk $D$, assumes every complex value with at most one exception on infinite su...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2005-07, Vol.139 (1), p.149-159
Main Author: COSTAKIS, GEORGE
Format: Article
Language:English
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Summary:By investigating the relation between growth and value distribution A. Melas established a qualitative version of a Picard type theorem for universal Taylor series, that is: every universal Taylor series on the open unit disk $D$, assumes every complex value with at most one exception on infinite subsets of $D$ that approach the boundary of $D$ rather slowly. On the other hand, we show that there are universal Taylor series on $D$ such that the infinite subset of $D$ on which exactly one value is assumed, can approach the boundary of $D$ arbitrarily fast. Hence in view of Melas' work our result is the best possible. We also study the problem of interpolation by universal Taylor series.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004105008406