Domains of Existence for Finely Holomorphic Functions

TY - JOUR

T1 - Domains of Existence for Finely Holomorphic Functions

AU - Fuglede, Bent

AU - Groot, Alan

AU - Wiegerinck, Jan

PY - 2019/10/1

Y1 - 2019/10/1

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

SN - 0926-2601

VL - 51

SP - 469

EP - 481

JO - Potential Analysis

JF - Potential Analysis

IS - 3

ER -