On the extreme points of some sets of analytic functions

Milcetich, John G.

doi:10.1090/S0002-9939-1974-0352470-X

On the extreme points of some sets of analytic functions
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by John G. Milcetich PDF

Proc. Amer. Math. Soc. 45 (1974), 223-228 Request permission

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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