Extreme and exposed representing measures of the disk algebra

• Autorzy: Alex Heinis , Jan Wiegerinck
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

exposed point; representing measure; extreme point; disk algebra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 73
• Numer: 2
• Strony: 105-118

Daty

wydano

2000

otrzymano

1998-06-18

poprawiono

1999-11-17

Twórcy

autor

Alex Heinis

• Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands

autor

Jan Wiegerinck

• Korteweg-de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands

Bibliografia

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• [2] R. Brummelhuis and J. Wiegerinck, Representing measures for the disc algebra and the ball algebra, Ann. Polon. Math. 55 (1991), 19-35.
• [3] T. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969.
• [4] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
• [5] A. J. Izzo, Exposed points in the set of representing measures for the disc algebra, Ann. Polon. Math. 61 (1995), 59-62.
• [6] P. Koosis, Theory of $H^p$ Spaces, Cambridge Univ. Press, Cambridge, 1980.
• [7] J. Ryff, The support of representing measures for the disc algebra, in: Function Algebras, F. Birtel (ed.), Scott, Foresman and Co., Glenview, 1966, 112-117.