Domains of Existence for Finely Holomorphic Functions

Bent Fuglede*, Alan Groot, Jan Wiegerinck

*Corresponding author af dette arbejde

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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.

OriginalsprogEngelsk
TidsskriftPotential Analysis
Vol/bind51
Udgave nummer3
Sider (fra-til)469–481
ISSN0926-2601
DOI
StatusUdgivet - 2019

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