Geodesic
Extreme and exposed representing measures of the disk algebra
Annales Polonici Mathematici, Tome 73 (2000) no. 2, pp. 105-118

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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.
DOI : 10.4064/ap-73-2-105-118
Keywords: exposed point, representing measure, extreme point, disk algebra

Alex Heinis 1 ; Jan Wiegerinck 1

1 
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Alex Heinis; Jan Wiegerinck. Extreme and exposed representing measures of the disk algebra. Annales Polonici Mathematici, Tome 73 (2000) no. 2, pp. 105-118. doi: 10.4064/ap-73-2-105-118

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