2017/01/03 by V. Nestoridis, Nestoridis, V.
Mathematics · #30D45 (Secondary) #32T05 (Primary) #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1701.00734
openalex publication_date 2017/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a simple and more elementary proof that the notions of Domain of Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on a combination of Baire's Category Theorem and Montel's Theorem. We also obtain generalizations by demanding that the non-extentable functions belong to a particular class of holomorphic functions in the domain. We give an example of a domain in the plane which is a domain of holomorphy with respect to the class of all holomorphic functions but not with respect to the class of holomorphic functions continuously extendable on the closure of the domain.