Domains of Existence for Finely Holomorphic Functions

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Standard

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 tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Fuglede, B, Groot, A & Wiegerinck, J 2019, 'Domains of Existence for Finely Holomorphic Functions', Potential Analysis, bind 51, nr. 3, s. 469–481. https://doi.org/10.1007/s11118-018-9719-1

APA

Fuglede, B., Groot, A., & Wiegerinck, J. (2019). Domains of Existence for Finely Holomorphic Functions. Potential Analysis, 51(3), 469–481. https://doi.org/10.1007/s11118-018-9719-1

Vancouver

Fuglede B, Groot A, Wiegerinck J. Domains of Existence for Finely Holomorphic Functions. Potential Analysis. 2019;51(3):469–481. https://doi.org/10.1007/s11118-018-9719-1

Author

Fuglede, Bent ; Groot, Alan ; Wiegerinck, Jan. / Domains of Existence for Finely Holomorphic Functions. I: Potential Analysis. 2019 ; Bind 51, Nr. 3. s. 469–481.

Bibtex

@article{146ef25ea3654d108551b0e75f26009c,
title = "Domains of Existence for Finely Holomorphic Functions",
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 = "Domain of existence, Finely holomorphic function",
author = "Bent Fuglede and Alan Groot and Jan Wiegerinck",
year = "2019",
doi = "10.1007/s11118-018-9719-1",
language = "English",
volume = "51",
pages = "469–481",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer",
number = "3",

}

RIS

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