ArticleOriginal scientific text
Title
Extreme and exposed representing measures of the disk algebra
Authors 1, 2
Affiliations
- Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
- Korteweg-de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Abstract
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.
Keywords
exposed point, representing measure, extreme point, disk algebra
Bibliography
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Pages:
105-118
Main language of publication
English
Received
1998-06-18
Accepted
1999-11-17
Published
2000
Exact and natural sciences