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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.09267 |
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| _version_ | 1866909082610302976 |
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| author | Sclosa, Davide |
| author_facet | Sclosa, Davide |
| contents | We investigate power series that converge to a bounded function on the real line. First, we establish relations between coefficients of a power series and boundedness of the resulting function; in particular, we show that boundedness can be prevented by certain Turán inequalities and, in the case of real coefficients, by certain sign patterns. Second, we show that the set of bounded power series naturally supports three topologies and that these topologies are inequivalent and incomplete. In each case, we determine the topological completion. Third, we study the algebra of bounded power series, revealing the key role of the backward shift operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09267 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounded Power Series on the Real Line Sclosa, Davide Classical Analysis and ODEs 30H05 (Primary), 30B10, 13J05 (Secondary) We investigate power series that converge to a bounded function on the real line. First, we establish relations between coefficients of a power series and boundedness of the resulting function; in particular, we show that boundedness can be prevented by certain Turán inequalities and, in the case of real coefficients, by certain sign patterns. Second, we show that the set of bounded power series naturally supports three topologies and that these topologies are inequivalent and incomplete. In each case, we determine the topological completion. Third, we study the algebra of bounded power series, revealing the key role of the backward shift operator. |
| title | Bounded Power Series on the Real Line |
| topic | Classical Analysis and ODEs 30H05 (Primary), 30B10, 13J05 (Secondary) |
| url | https://arxiv.org/abs/2312.09267 |