Sur la frontière de Shilov des domaines de \({\mathbb{C}}^ n\)
Given \(n\geq 1\), we construct a circled bounded domain \(\Omega\) in \({\mathbb{C}}^ n\) such that (i) \({\bar \Omega}\) is polynomially convex, (ii) the Shilov boundary of \({\bar \Omega}\) with respect to the algebra P(\({\bar \Omega}\)) is of Hausdorff dimension 1. This answers a question of \textit{A. G. Vituškin} [cf. Sov. Math., Dokl. 14(1973), 1618-1619 (1974); translation from Dokl. Math. Nauk SSSR 213, 14-15 (1973; Zbl 0292.32011)].
scientific article; zbMATH DE number 3914706