Positive harmonic functions on Denjoy domains in the complex plane

Abstract

Let Ω be a domain in the complex plane C whose complement E=\(\overline C \backslash \Omega \) is a subset of the real line (i.e., Ω a Denjoy domain). If each point of E is regular for the Dirichlet problem in Ω, we provide a geometric description of the structure of E near infinity such that the Martin boundary of Ω has one or two “infinite” points.