Positive Harmonic Functions on Denjoy Domains in the Complex Plane

Abstract

Let Ω be a domain in the complex plane C whose complement E = C \ Ω, where C = C ∪ {∞} is a subset of the real line (i.e. Ω is 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.

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