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Proceedings of the American Mathematical Society

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

 

 

Extreme points of a class of subordinate functions


Author: T. Sheil-Small
Journal: Proc. Amer. Math. Soc. 91 (1984), 73-74
MSC: Primary 30C80
DOI: https://doi.org/10.1090/S0002-9939-1984-0735567-8
MathSciNet review: 735567
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Abstract: It is shown that, if $ F\left( z \right)$ is subordinate to $ H\left( {\left( {1 + z} \right) / \left( {1 - z} \right)} \right)$ in the unit disc, where $ H\left( w \right)$ is a quadratic polynomial for which $ H'\left( w \right) \ne 0$ in the right half-plane, then

$\displaystyle F\left( z \right) = \int\limits_T {H\left( {\frac{{1 + z{e^{ - it}}}}{{1 - z{e^{ - it}}}}} \right)d\mu } $

for a suitable probability measure $ \mu $ on the unit circle $ T$.

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DOI: https://doi.org/10.1090/S0002-9939-1984-0735567-8
Article copyright: © Copyright 1984 American Mathematical Society