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 | References | Similar Articles | Additional Information

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 $|\operatorname {Re} f(z)| < \pi /2$ are determined. Also a partial characterization is given for the extreme points of ${G_\alpha } = \{ f\epsilon A:f(0) = 1$ and $|\arg f(z)| < \alpha \pi /2\} ,0 < \alpha < 1$.

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Keywords:
Extreme points,
subordination,
<IMG WIDTH="33" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${H^p}$"> spaces

Article copyright:
© Copyright 1974
American Mathematical Society