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Transactions of the American Mathematical Society

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Complex approximation for vector-valued functions with an application to boundary behaviour


Authors: Leon Brown, P. M. Gauthier and W. Seidel
Journal: Trans. Amer. Math. Soc. 191 (1974), 149-163
MSC: Primary 30A82
DOI: https://doi.org/10.1090/S0002-9947-1974-0342707-X
MathSciNet review: 0342707
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Abstract: This paper deals with the qualitative theory of uniform approximation by holomorphic functions. The first theorem is an extension to vector-valued mappings of N. U. Arakélian's theorem on uniform holomorphic approximation on closed sets. Our second theorem is on asymptotic approximation and yields, as in the scalar case, applications to cluster sets.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0342707-X
Article copyright: © Copyright 1974 American Mathematical Society

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