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Proceedings of the American Mathematical Society

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

 

 

Best uniform approximation by bounded analytic functions


Author: M. Papadimitrakis
Journal: Proc. Amer. Math. Soc. 103 (1988), 882-886
MSC: Primary 30E10; Secondary 30D50, 41A50
MathSciNet review: 947674
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Abstract: This paper gives a counterexample to the conjecture that the continuity of the conjugate $ \tilde f$ of an $ f \in C\left( T \right)$ implies the continuity of the best uniform approximation $ g \in {H^\infty }\left( T \right)$ of $ f$. It also states two conditions which imply the continuity of $ g$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0947674-9
Article copyright: © Copyright 1988 American Mathematical Society