Carleman approximation by non-critical functions on Riemann surfaces
arXiv:2508.05765 · doi:10.1007/s13324-025-01157-4
Abstract
We present the class of semi-admissible subsets of an open Riemann surface on which Carleman approximation by non-critical holomorphic functions is possible. In particular we characterize closed sets with empty interior on which continuous functions can be approximated by non-critical holomorphic ones. We also consider a different approach, which in some cases gives uniform approximation by non-critical holomorphic functions on more general sets than semi-admissible ones.
arXiv comment13 pages, 2 figures. Title changed. Minor revisions to address typos and improve the exposition. To appear in the journal Analysis and Mathematical Physics