A zero set for \(A^{\infty}(D)\) of Hausdorff dimension \(2n-1\) (Q1093054)

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.