Plurisubharmonic and holomorphic functions relative to the plurifine topology

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Standard

Plurisubharmonic and holomorphic functions relative to the plurifine topology. / El Kadiri, M.; Fuglede, Bent; Wiegerinck, J.

I: Journal of Mathematical Analysis and Applications, Bind 381, Nr. 2, 2011, s. 706-723.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

El Kadiri, M, Fuglede, B & Wiegerinck, J 2011, 'Plurisubharmonic and holomorphic functions relative to the plurifine topology', Journal of Mathematical Analysis and Applications, bind 381, nr. 2, s. 706-723. https://doi.org/10.1016/j.jmaa.2011.03.041

APA

El Kadiri, M., Fuglede, B., & Wiegerinck, J. (2011). Plurisubharmonic and holomorphic functions relative to the plurifine topology. Journal of Mathematical Analysis and Applications, 381(2), 706-723. https://doi.org/10.1016/j.jmaa.2011.03.041

Vancouver

El Kadiri M, Fuglede B, Wiegerinck J. Plurisubharmonic and holomorphic functions relative to the plurifine topology. Journal of Mathematical Analysis and Applications. 2011;381(2):706-723. https://doi.org/10.1016/j.jmaa.2011.03.041

Author

El Kadiri, M. ; Fuglede, Bent ; Wiegerinck, J. / Plurisubharmonic and holomorphic functions relative to the plurifine topology. I: Journal of Mathematical Analysis and Applications. 2011 ; Bind 381, Nr. 2. s. 706-723.

Bibtex

@article{1d7cab43f1d04cd7ac3310ae9948937d,
title = "Plurisubharmonic and holomorphic functions relative to the plurifine topology",
abstract = "A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only if it is locally bounded from above in the plurifine topology and f∘h is finely subharmonic for all complex affine-linear maps h. As a consequence, the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic, and it differs from the pointwise supremum at most on a pluripolar set. Weak plurifine plurisubharmonicity and weak plurifine holomorphy are preserved under composition with weakly plurifinely holomorphic maps.",
author = "{El Kadiri}, M. and Bent Fuglede and J. Wiegerinck",
year = "2011",
doi = "10.1016/j.jmaa.2011.03.041",
language = "English",
volume = "381",
pages = "706--723",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press",
number = "2",

}

RIS

TY - JOUR

T1 - Plurisubharmonic and holomorphic functions relative to the plurifine topology

AU - El Kadiri, M.

AU - Fuglede, Bent

AU - Wiegerinck, J.

PY - 2011

Y1 - 2011

N2 - A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only if it is locally bounded from above in the plurifine topology and f∘h is finely subharmonic for all complex affine-linear maps h. As a consequence, the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic, and it differs from the pointwise supremum at most on a pluripolar set. Weak plurifine plurisubharmonicity and weak plurifine holomorphy are preserved under composition with weakly plurifinely holomorphic maps.

AB - A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only if it is locally bounded from above in the plurifine topology and f∘h is finely subharmonic for all complex affine-linear maps h. As a consequence, the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic, and it differs from the pointwise supremum at most on a pluripolar set. Weak plurifine plurisubharmonicity and weak plurifine holomorphy are preserved under composition with weakly plurifinely holomorphic maps.

U2 - 10.1016/j.jmaa.2011.03.041

DO - 10.1016/j.jmaa.2011.03.041

M3 - Journal article

VL - 381

SP - 706

EP - 723

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

ID: 37567709