Gauthier, Paul M.; Sharifi, Fatemeh Luzin-type holomorphic approximation on closed subsets of open Riemann surfaces. (English) Zbl 1369.30039 Can. Math. Bull. 60, No. 2, 300-308 (2017). Summary: It is known that if \(E\) is a closed subset of an open Riemann surface \(R\) and \(f\) is a holomorphic function on a neighbourhood of \(E,\) then it is “usually” not possible to approximate \(f\) uniformly by functions holomorphic on all of \(R\). We show, however, that for every open Riemann surface \(R\) and every closed subset \(E\subset R,\) there is closed subset \(F\subset E,\) which approximates \(E\) extremely well, such that every function holomorphic on \(F\) can be approximated much better than uniformly by functions holomorphic on \(R\). Cited in 3 Documents MSC: 30E15 Asymptotic representations in the complex plane 30F99 Riemann surfaces Keywords:Carleman approximation; tangential approximation; Myrberg surface PDFBibTeX XMLCite \textit{P. M. Gauthier} and \textit{F. Sharifi}, Can. Math. Bull. 60, No. 2, 300--308 (2017; Zbl 1369.30039) Full Text: DOI