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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Martin compactifications of the punctured disk with close to rotation free densities


Author: Toshimasa Tada
Journal: Proc. Amer. Math. Soc. 103 (1988), 483-486
MSC: Primary 31C35; Secondary 30F25
DOI: https://doi.org/10.1090/S0002-9939-1988-0943071-0
MathSciNet review: 943071
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Abstract: The purpose of this paper is to prove that Martin compactifications $ \Omega _P^*$ and $ \Omega _Q^*$ of the punctured unit disk $ \Omega :0 < \vert z\vert < 1$ with respect to equations $ \Delta u = Pu$ and $ \Delta u = Qu$, respectively, are homeomorphic to each other if $ \vert P(z) - Q(z)\vert = O(\vert z{\vert^{ - 2}})(z \to 0)$ and $ P(z) = P(\vert z\vert)(z \in \Omega )$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943071-0
Article copyright: © Copyright 1988 American Mathematical Society