Universal partial sums of Taylor series as functions of the centre of expansion

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2 Citations (SciVal)

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 languageEnglish
Pages (from-to)306-315
Number of pages10
JournalComplex Variables and Elliptic Equations
Volume65
Issue number2
DOIs
Publication statusPublished - 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.

FundersFunder number
Horizon 2020 Framework Programme
European Research Council
Horizon 2020639046

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

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