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Plurifine potential theory

100%
Wiegerinck J.
Annales Polonici Mathematici
|
2012
|
tom 106
|
nr 1
275-292
EN
We give an overview of the recent developments in plurifine pluripotential theory, i.e. the theory of plurifinely plurisubharmonic functions.
2
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Extreme and exposed representing measures of the disk algebra

64%
Heinis A., Wiegerinck J.
Annales Polonici Mathematici
|
2000
|
tom 73
|
nr 2
105-118
EN
We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed and show that so-called BSZ-measures are never exposed.
3
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Le cône des fonctions plurisousharmoniques négatives et une conjecture de Coman

64%
Carlehed M., Wiegerinck J.
Annales Polonici Mathematici
|
2003
|
tom 80
|
nr 1
93-108
FR
Les fonctions plurisousharmoniques négatives dans un domaine Ω de ℂⁿ forment un cône convexe. Nous considérons les points extrémaux de ce cône, et donnons trois exemples. En particulier, nous traitons le cas de la fonction de Green pluricomplexe. Nous calculons celle du bidisque, lorsque les pôles se situent sur un axe. Nous montrons que cette fonction ne coïncide pas avec la fonction de Lempert correspondante. Cela donne un contre-exemple à une conjecture de Dan Coman.
4
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Representing measures for the disc algebra and for the ball algebra

64%
Brummelhuis R., Wiegerinck J.
Annales Polonici Mathematici
|
1991
|
tom 55
|
nr 1
19-35
EN
We consider the set of representing measures at 0 for the disc and the ball algebra. The structure of the extreme elements of these sets is investigated. We give particular attention to representing measures for the 2-ball algebra which arise by lifting representing measures for the disc algebra.
5
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Graphs with multiple sheeted pluripolar hulls

64%
Poletsky E., Wiegerinck J.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 2
161-171
EN
We study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.
6
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The image of a finely holomorphic map is pluripolar

51%
Edigarian A., El Marzguioui S., Wiegerinck J.
Annales Polonici Mathematici
|
2010
|
tom 97
|
nr 2
137-149
EN
We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.
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