Martin Compactifications of the Punctured Disk with Close to Rotation Free Densities

Abstract

The purpose of this paper is to prove that Martin compactifications $\Omega _P^*$ and $\Omega _Q^*$ of the punctured unit disk $\Omega :0 < |z| < 1$ with respect to equations $\Delta u = Pu$ and $\Delta u = Qu$, respectively, are homeomorphic to each other if $|P(z) - Q(z)| = O(|z{|^{ - 2}})(z \to 0)$ and $P(z) = P(|z|)(z \in \Omega )$.