Holomorphic extendibility and the argument principle

Details Holomorphic extendibility and the argument principle Holomorphic extendibility and the argument principle

2004-03-25

arxiv.org/abs/math/0403446v1

Mathematics

Complex Variables

To appear in "Complex Analysis and Dynamical Systems II (Proceedings of a conference held in honor of Professor Lawrence Zalcm

Scientific paper

The paper gives the following characterization of the disc algebra in terms
of the argument principle: A continuous function f on the unit circle T extends
holomorphically through the unit disc if and only if for each polynomial P such
that f+P has no zero on T the change of argument of f+P around T is
nonnegative.

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