Polynomials of an inner function which are exposed points in 𝐻¹

Inoue, Jyunji; Nakazi, Takahiko

doi:10.1090/S0002-9939-1987-0891144-2

Polynomials of an inner function which are exposed points in $H^ 1$
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by Jyunji Inoue and Takahiko Nakazi PDF

Proc. Amer. Math. Soc. 100 (1987), 454-456 Request permission

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 $p\left ( z \right )/{\left \| {p\left ( z \right )} \right \|_1}$ 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 ${\left \| f \right \|_\infty } \leqslant 1$, $p\left ( f \right )/{\left \| {p\left ( f \right )} \right \|_1}$ is also an exposed point.

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