Best uniform approximation by bounded analytic functions
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- by M. Papadimitrakis PDF
- Proc. Amer. Math. Soc. 103 (1988), 882-886 Request permission
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 $g$.References
- Lennart Carleson and Sigvard Jacobs, Best uniform approximation by analytic functions, Ark. Mat. 10 (1972), 219–229. MR 322410, DOI 10.1007/BF02384810
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 882-886
- MSC: Primary 30E10; Secondary 30D50, 41A50
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947674-9
- MathSciNet review: 947674