Universal Laurent series in finitely connected domains
For a simply connected domain in the complex plane \(\mathbb{C}\), \textit{A. D. Melas} and \textit{V. Nestoridis} [Adv. Math. 157, No. 2, 138--176 (2001; Zbl 0985.30023)] discussed the existence of universal Taylor series. Then \textit{G. Costakis, V. Nestoridis}, and \textit{I. Papadoperakis} [Proc. Edinb. Math. Soc. (2) 48, No. 3, 571--583 (2005; Zbl 1151.30301)] replaced Taylor series by Laurent series and considered the existence of universal Laurent series. Let \(\Omega\) be a finitely connected domain in \(\mathbb{C}\), and assume that \((\mathbb{C}\cup {\infty})\setminus \Omega\) has finitely many components, the paper under review proves that it is possible to demand universal approximation to a part of the boundary \(\partial \Omega\) while on the remaining part the universal function can be smooth.
scientific article; zbMATH DE number 5343873
scientific article