Holomorphic Extendibility and Mapping Degree

Details Holomorphic Extendibility and Mapping Degree Holomorphic Extendibility and Mapping Degree

2006-06-13

arxiv.org/abs/math/0606306v1

Mathematics

Complex Variables

8 pages, to appear in Proc.Roy.Soc.Edinb.Sect A

Scientific paper

Let D be a bounded, finitely connected domain in the complex plane without isolated points in the boundary and let f be a continuous function on the boundary bD. Let F be a continuous extension of f to the closure of D. We prove that f extends holomorphically through D if and only if the degree of F+h is nonnegative for every holomorphic function h on D such that F+h is bounded away from zero near bD.

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