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A zero set for \(A^{\infty}(D)\) of Hausdorff dimension \(2n-1\). (English) Zbl 0628.32017
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.
Reviewer: C.Berenstein

MSC:
32A38 Algebras of holomorphic functions of several complex variables
32A40 Boundary behavior of holomorphic functions of several complex variables
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