ABSTRACT
If an open subset D⊆ ℂ n is not a domain of holomorphy, then by Theorem G7 there is at least one point A ∈ ∂D through which all functions f ∈ O D https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203750063/1087b710-7222-48dd-8094-26eaf896ae1b/content/eq1266.tif"/> can simultaneously be extended. One might expect that there is a maximal open subset E ⊆ ℂ n containing D and such that every f ∈ O D https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203750063/1087b710-7222-48dd-8094-26eaf896ae1b/content/eq1267.tif"/> extends to a holomorphic function in E. For various special classes of subsets D there do exist easily described maximal sets E for which such extension is possible.
