Single valued conjugates and holomorphic extendibility
Complex Variables
2007-05-23 v1
Abstract
Let D be a bounded domain in the complex plane whose boundary consists of m pairwise disjoint simple closed curves where m is greater than one. Let A(bD) be the algebra of all continuous functions on bD which extend holomorphically through D. We show that a continuous function f on bD belongs to A(bD) if for each g in A(bD) the harmonic extension of Re(fg) to D has a single valued conjugate.
Cite
@article{arxiv.math/0507100,
title = {Single valued conjugates and holomorphic extendibility},
author = {Josip Globevnik},
journal= {arXiv preprint arXiv:math/0507100},
year = {2007}
}
Comments
4 pages, to appear in Proc.Roy.Soc.Edinb.Sec.A