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## Annales Polonici Mathematici

2000 | 73 | 2 | 105-118
Tytuł artykułu

### Extreme and exposed representing measures of the disk algebra

Autorzy
Treść / Zawartość
Warianty tytułu
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
Czasopismo
Rocznik
Tom
Numer
Strony
105-118
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-06-18
poprawiono
1999-11-17
Twórcy
autor
• Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
autor
• Korteweg-de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Bibliografia
• [1] L. Brown, A. Shields and K. Zeller, On absolutely convergent exponential sums, Trans. Amer. Math. Soc. 96 (1960), 162-183.
• [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.
Typ dokumentu
Bibliografia
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