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

Brown, Leon; Gauthier, P. M.; Seidel, W.

doi:10.1090/S0002-9947-1974-0342707-X

Complex approximation for vector-valued functions with an application to boundary behaviour
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by Leon Brown, P. M. Gauthier and W. Seidel PDF

Trans. Amer. Math. Soc. 191 (1974), 149-163 Request permission

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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