Generic power series on subsets of the unit disk

Balázs Maga; Péter Maga

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arXiv · 2101.08654

Generic power series on subsets of the unit disk

Balázs Maga·Péter Maga

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Abstract

In this paper, we examine the boundary behaviour of the generic power series $f$ with coefficients chosen from a fixed bounded set $\Lambda$ in the sense of Baire category. Notably, we prove that for any open subset $U$ of the unit disk $D$ with a non-real boundary point on the unit circle, $f(U)$ is a dense set of $\CC$. As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given.

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Balázs Maga, Péter Maga. 2021-01-21. Generic power series on subsets of the unit disk. https://arxiv.org/abs/2101.08654

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