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Keywords:
complex power series; boundary behaviour; Baire category
complex power series; boundary behaviour; Baire category
Summary:
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 nonreal boundary point on the unit circle, $f(U)$ is a dense set of $\mathbb {C}$. 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.
References:
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