Domains of Existence for Finely Holomorphic Functions

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Bent Fuglede, Alan Groot, Jan Wiegerinck

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.

Original languageEnglish
JournalPotential Analysis
Publication statusE-pub ahead of print - 2019

    Research areas

  • Domain of existence, Finely holomorphic function

ID: 203665499