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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the extreme points of some sets of analytic functions


Author: John G. Milcetich
Journal: Proc. Amer. Math. Soc. 45 (1974), 223-228
MSC: Primary 30A76
DOI: https://doi.org/10.1090/S0002-9939-1974-0352470-X
MathSciNet review: 0352470
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Abstract: Let $ A$ denote the set of analytic functions defined on the open unit disc. The extreme points of $ F = \{ f \epsilon A:f(0) = 0$ and $ \vert\operatorname{Re} f(z)\vert < \pi /2$ are determined. Also a partial characterization is given for the extreme points of $ {G_\alpha } = \{ f\epsilon A:f(0) = 1$ and $ \vert\arg f(z)\vert < \alpha \pi /2\} ,0 < \alpha < 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0352470-X
Keywords: Extreme points, subordination, $ {H^p}$ spaces
Article copyright: © Copyright 1974 American Mathematical Society