The argument principle and holomorphic extendibility

Details The argument principle and holomorphic extendibility The argument principle and holomorphic extendibility

2004-05-21

arxiv.org/abs/math/0405409v1

Mathematics

Complex Variables

10 pages, to appear in J.d'Analyse Math

Scientific paper

Let D be a bounded domain in the complex plane whose boundary consists of finitely many pairwise disjoint simple closed curves. Give bD the standard orientation and let A(D) be the algebra of all continuous functions on the closure of D which are holomorphic on D. In the paper we prove that a continuous function f on bD extends to a function in A(D) if and only if for each g in A(D) such that f+g has no zero on bD the change of argument of f+g along bD is nonnegative.

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