Plurisubharmonic and holomorphic functions relative to the plurifine topology
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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
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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