Positive Harmonic Functions on Denjoy Domains in the Complex Plane

Details Positive Harmonic Functions on Denjoy Domains in the Complex Plane Positive Harmonic Functions on Denjoy Domains in the Complex Plane

2006-08-25

arxiv.org/abs/math/0608643v1

Mathematics

Complex Variables

Scientific paper

Let $\Om$ be a domain in the complex plane $\C$ whose complement $E=\OC\setminus \Om$, where $\OC=\C\cup\{\infty\}$ is a subset of the real line (i.e. $\Om$ is a Denjoy domain). If each point of $E$ is regular for the Dirichlet problem in $\Om$, we provide a geometric description of the structure of $E$ near infinity such that the Martin boundary of $\Om$ has one or two "infinite" points.

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