2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70597The 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.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.MathComplex Variablestext