Abstract
V. Nestoridis conjectured that if Ω is a simply connected domain of C that does not contain 0 and S(Ω) is the set of all functions f ∈ H(Ω) with the property that the set (Formula presented.) is dense in (Formula presented.), then (Formula presented.) is a dense H(Ω) set in S(Ω). We answer the conjecture in the affirmative in the special case where Ω is an open disc D(z0, r) that does not contain 0.
Original language | English |
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Pages (from-to) | 306-315 |
Number of pages | 10 |
Journal | Complex Variables and Elliptic Equations |
Volume | 65 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Feb 2020 |
Bibliographical note
Publisher Copyright:© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Funding
This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [grant agreement no. 639046]. I would like to thank V. Nestoridis, E. Archer and G. Vasdekis for taking interest in this work. I would also like to thank E. Katsoprinakis and the anonymous referees for their suggestions and comments.
Funders | Funder number |
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Horizon 2020 Framework Programme | |
European Research Council | |
Horizon 2020 | 639046 |
Keywords
- 30K05
- 30K99
- baire's category theorem
- generic property
- ostrowski-gaps
- partial sums
- S. Ivashkovich
- Taylor expansion
- universal taylor series
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics