An interpolation characterization of domains of holomorphy
The goal of this note is the following: Theorem. Let \(\Omega \subset \mathbb{C}^n\) be a domain. Then \(\Omega\) is a domain of holomorphy if and only if for any sequence of distinct points \(\{p^{(k)}\}^\infty_{k=1} \subset \Omega\) without limit points \(\Omega\), and any sequence of complex numbers \(\{A_k\}^\infty_{k=1}\), there exists a holomorphic function \(f\) in \(\Omega\) such that \(f(p^{(k)}) =A_k\), \(\forall k\in \mathbb{N}\).
scientific article; zbMATH DE number 1159082