Peak sets in pseudoconvex domains with isolated degeneracies
Let D be a bounded domain in \({\mathbb{C}}^ n\) with smooth boundary and \(A^{\infty}(D)\) the set of holomorphic functions in D which have a \(C^{\infty}\) extension to \(\bar D\). If D is strictly pseudoconvex, \textit{J.Chaumat} and \textit{A.-M. Chollet} proved that every compact subset of a peak set for \(A^{\infty}(D)\) is a peak set for \(A^{\infty}(D)\). The result was extended by \textit{A. V. Noell} to bounded pseudoconvex domains of finite type in \({\mathbb{C}}^ 2\). Here, we prove that the result is also true for bounded pseudoconvex domains in \({\mathbb{C}}^ n\) with smooth boundary, which are strictly pseudoconvex except at a finite number of points. The methods used in the paper are generalizations of those used by Chaumat and Chollet to prove the assertion in the strictly pseudoconvex case.
scientific article; zbMATH DE number 3871766