A zero set for \(A^{\infty}(D)\) of Hausdorff dimension \(2n-1\) (Q1093054)
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scientific article; zbMATH DE number 4021580
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A zero set for \(A^{\infty}(D)\) of Hausdorff dimension \(2n-1\) |
scientific article; zbMATH DE number 4021580 |
Statements
A zero set for \(A^{\infty}(D)\) of Hausdorff dimension \(2n-1\) (English)
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1987
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Given a strongly pseudoconvex domain D with \(C^{\infty}\) boundary in \({\mathbb{C}}^ n\), the author constructs a closed subset F of \(\partial D\) with Hausdorff dimension \(2n-1\) such that there is a function \(f\in A^{\infty}(D)\) with \(F=\{p\in \bar D:\) \(f(p)=0\}\) and f vanishes of infinite order of F. The best previously known result was a construction of Chaumat and Chollet of sets of Hausdorff dimension n.
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A\({}^{\infty }\) functions
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peak set
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Hausdorff dimension
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