On the closed ideals inA(W)

Abstract

scription of the closed ideals in the disc algebra is shown to apply to an ideal whose hull meets the boundary of the domain in a finite union of analytic arcs. The canonical factorization into inner and outer functions in the disc is replaced by a potential theoretic decomposition theorem, thus allowing essentially the same description to be carried over. The basically local nature of the problem is used to reduce it to the previously known ideal theory of a compact bordered Riemann surface. This reduction is facilitated by a factorization theorem that is proved by potential theoretic methods.