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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
##### Keywords:
A$${}^{\infty }$$ functions; peak set; Hausdorff dimension
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