Title: | Generic power series on subsets of the unit disk (English) |
Author: | Maga, Balázs |
Author: | Maga, Péter |
Language: | English |
Journal: | Czechoslovak Mathematical Journal |
ISSN: | 0011-4642 (print) |
ISSN: | 1572-9141 (online) |
Volume: | 72 |
Issue: | 3 |
Year: | 2022 |
Pages: | 637-652 |
Summary lang: | English |
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Category: | math |
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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. (English) |
Keyword: | complex power series |
Keyword: | boundary behaviour |
Keyword: | Baire category |
MSC: | 28A05 |
MSC: | 30B30 |
MSC: | 54H05 |
idZBL: | Zbl 07584092 |
idMR: | MR4467932 |
DOI: | 10.21136/CMJ.2022.0021-21 |
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Date available: | 2022-08-22T08:15:42Z |
Last updated: | 2022-12-27 |
Stable URL: | http://hdl.handle.net/10338.dmlcz/150607 |
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Reference: | [1] : Bolyai János Mathematical Society: Miklós Schweitzer Memorial Competition 2020, Problems and Solutions.Available at \brokenlink{https://www.bolyai.hu/files/Schweitzer_{2020_megoldasok.pdf}} Hungarian. MR 1162554 |
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Reference: | [6] Kuratowski, K.: Topology. Vol. 1.Academic Press, New York (1966). Zbl 0158.40802, MR 0217751, 10.1016/C2013-0-11022-7 |
Reference: | [7] Maga, B., Maga, P.: Random power series near the endpoint of the convergence interval.Publ. Math. 93 (2018), 413-424. Zbl 1424.60048, MR 3875344, 10.5486/PMD.2018.8130 |
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