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Potential Analysis

, Volume 51, Issue 3, pp 469–481 | Cite as

Domains of Existence for Finely Holomorphic Functions

  • Bent FugledeEmail author
  • Alan Groot
  • Jan Wiegerinck
Open Access
Article
  • 135 Downloads

Abstract

We show that fine domains in ℂ with the property that they are Euclidean Fs and Gd, are in fact fine domains of existence for finely holomorphic functions. Moreover regular fine domains are also fine domains of existence. Next we show that fine domains such as ℂ \ ℚ or ℂ \ (ℚ × iℚ), more specifically fine domains V with the properties that their complement contains a non-empty polar set E that is of the first Baire category in its Euclidean closure K and that (K \ E) ⊂ V, are not fine domains of existence.

Keywords

Finely holomorphic function Domain of existence 

Mathematics Subject Classification (2010)

30G12 30A14 31C40 

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CopenhagenKøbenhavnDenmark
  2. 2.Analysis SectionKU LeuvenLeuvenBelgium
  3. 3.KdV Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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