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Proceedings of the American Mathematical Society

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

 

 

Polynomials of an inner function which are exposed points in $ H\sp 1$


Authors: Jyunji Inoue and Takahiko Nakazi
Journal: Proc. Amer. Math. Soc. 100 (1987), 454-456
MSC: Primary 30D55; Secondary 30D50, 46J15
MathSciNet review: 891144
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Abstract: It is known that if $ p\left( z \right)$ is an analytic polynomial which has no zeros in the open unit disc and distinct zeros in the unit circle, then $ p\left( z \right)/{\left\Vert {p\left( z \right)} \right\Vert _1}$ is an exposed point of the unit ball of the Hardy space $ {H^1}$.

In this paper, it is proved that for a bounded analytic function $ f$ with $ {\left\Vert f \right\Vert _\infty } \leqslant 1$, $ p\left( f \right)/{\left\Vert {p\left( f \right)} \right\Vert _1}$ is also an exposed point.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891144-2
Keywords: Exposed points, Hardy spaces, polynomials, inner functions
Article copyright: © Copyright 1987 American Mathematical Society