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arXiv · 0712.1039

The Corona Theorem on the Complements of Certain Square Cantor Sets

Jon Handy
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Abstract

Let $K$ be a square Cantor set, i.e. the Cartesian product $K=E\times E$ of two linear Cantor sets. Let $δ_n$ denote the proportion of the intervals removed in the $n$th stage of the construction of $E$. It is shown that if $δ_n=o(\frac1{\log\log n})$ then the corona theorem holds on the domain $Ω=\mathbb C^\ast\setminus K$.

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Jon Handy. 2007-12-06. The Corona Theorem on the Complements of Certain Square Cantor Sets. https://arxiv.org/abs/0712.1039

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