2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75684Let 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.4 pages, to appear in Proc.Roy.Soc.Edinb.Sec.AComplex Variablestext