Domains of Existence for Finely Holomorphic Functions
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Domains of Existence for Finely Holomorphic Functions. / Fuglede, Bent; Groot, Alan; Wiegerinck, Jan.
I: Potential Analysis, Bind 51, Nr. 3, 2019, s. 469–481.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt
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TY - JOUR
T1 - Domains of Existence for Finely Holomorphic Functions
AU - Fuglede, Bent
AU - Groot, Alan
AU - Wiegerinck, Jan
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Domain of existence
KW - Finely holomorphic function
UR - http://www.scopus.com/inward/record.url?scp=85051683981&partnerID=8YFLogxK
U2 - 10.1007/s11118-018-9719-1
DO - 10.1007/s11118-018-9719-1
M3 - Journal article
AN - SCOPUS:85051683981
VL - 51
SP - 469
EP - 481
JO - Potential Analysis
JF - Potential Analysis
SN - 0926-2601
IS - 3
ER -
ID: 203665499