Extreme and exposed representing measures of the disk algebra

Volume 73 / 2000

Alex Heinis, Jan Wiegerinck Annales Polonici Mathematici 73 (2000), 105-118 DOI: 10.4064/ap-73-2-105-118


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.


  • Alex Heinis
  • Jan Wiegerinck

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