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Proceedings of the American Mathematical Society

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

 

 

Picard dimensions of close to rotationally invariant densities


Author: Toshimasa Tada
Journal: Proc. Amer. Math. Soc. 100 (1987), 467-473
MSC: Primary 31A35; Secondary 30F20, 31C35
DOI: https://doi.org/10.1090/S0002-9939-1987-0891147-8
MathSciNet review: 891147
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Abstract: The purpose of this paper is to show that the Picard dimensions of a rotation-free density $ P$ and a general density $ Q$ on the punctured unit disk $ 0 < \left\vert z \right\vert < 1$ are equal to each other if $ \left\vert {P\left( z \right) - Q\left( z \right)} \right\vert = O\left( {{{\left\vert z \right\vert}^{ - 2}}} \right)$ as $ z \to 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891147-8
Keywords: Picard dimension and principle, Martin boundary
Article copyright: © Copyright 1987 American Mathematical Society