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Plurifine potential theory

Jan Wiegerinck — 2012

Annales Polonici Mathematici

We give an overview of the recent developments in plurifine pluripotential theory, i.e. the theory of plurifinely plurisubharmonic functions.

Extreme and exposed representing measures of the disk algebra

Alex HeinisJan Wiegerinck — 2000

Annales Polonici Mathematici

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...

Le cône des fonctions plurisousharmoniques négatives et une conjecture de Coman

Magnus CarlehedJan Wiegerinck — 2003

Annales Polonici Mathematici

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.

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