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Proceedings of the American Mathematical Society

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

 

 

The Rudin-Carleson theorem for vector-valued functions


Author: J. Globevnik
Journal: Proc. Amer. Math. Soc. 53 (1975), 250-252
MSC: Primary 46J15; Secondary 30A98
DOI: https://doi.org/10.1090/S0002-9939-1975-0383083-2
MathSciNet review: 0383083
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Abstract: The following generalization of the Rudin-Carleson theorem is proved. Let $ X$ be a complex Banach space and let $ f:F \to X$ be a continuous function, where $ F$ is a closed subset of the unit circle in $ C$ of Lebesgue measure zero. There exists a continuous function $ g$ from the closed unit disc to $ X$ which is analytic on the open unit disc and satisfies (i) $ g\vert F = f$, (ii) $ {\max _{\vert z\vert \leqslant 1}}\vert\vert g(z)\vert\vert = {\max _{z\epsilon F}}\vert\vert f(z)\vert\vert$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0383083-2
Article copyright: © Copyright 1975 American Mathematical Society