Holomorphic extendibility and the argument principle
Complex Variables
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0403446,
title = {Holomorphic extendibility and the argument principle},
author = {Josip Globevnik},
journal= {arXiv preprint arXiv:math/0403446},
year = {2007}
}
Comments
To appear in "Complex Analysis and Dynamical Systems II (Proceedings of a conference held in honor of Professor Lawrence Zalcman's sixtieth birthday in Nahariya, Israel, June 9-12, 2003)", Contemp.Math