English

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.

Keywords

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