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Proceedings of the American Mathematical Society

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A maximum principle for quotient norms in $ H\sp \infty$


Author: Eric Hayashi
Journal: Proc. Amer. Math. Soc. 99 (1987), 323-327
MSC: Primary 30E10; Secondary 30C15, 30D50
DOI: https://doi.org/10.1090/S0002-9939-1987-0870794-3
MathSciNet review: 870794
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Abstract: Let $ G$ be a closed subset of the open unit disk $ D$ in the complex plane, and let $ p$ denote a general polynomial of degree $ n$ which has all of its roots in $ G$. For a fixed $ h$ in $ {H^\infty },\vert\vert h - p{H^\infty }\vert{\vert _{{H^\infty }/p{H^\infty }}}$ is maximized only if all the zeros of $ p$ are on the boundary of $ G$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0870794-3
Article copyright: © Copyright 1987 American Mathematical Society