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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Analytic extensions and selections


Author: J. Globevnik
Journal: Trans. Amer. Math. Soc. 254 (1979), 171-177
MSC: Primary 46J10; Secondary 30H05
DOI: https://doi.org/10.1090/S0002-9947-1979-0539913-2
MathSciNet review: 539913
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Abstract: Let G be a closed subset of the closed unit disc in C, let F be a closed subset of the unit circle of measure 0 and let $ \Phi $ map G into the class of all open subsets of a complex Banach space X. Under suitable additional assumptions on $ \Phi $ we prove that given any continuous function $ f:\,F \to X$ satisfying $ f(z)\, \in \,{\text{closure(}}\Phi (z))\,(z\, \in \,F\, \cap \,G)$ there exists a continuous function f from the closed unit disc into X, analytic in the open unit disc, which extends f and satisfies $ \tilde f(z)\, \in \,\Phi (z)\,(z\, \in \,G\, - \,F)$. This enables us to generalize and sharpen known dominated extension theorems for the disc algebra.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0539913-2
Article copyright: © Copyright 1979 American Mathematical Society

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