Tyson Ritter
Associate Professor of the University of Stavanger.
Title: A Rudin-Carleson theorem with Runge approximation for maps into Oka manifolds
Abstract:
Given a closed set $E \subset \partial {\mathbb D}$ of measure zero and a continuous function $\varphi: E \to {\mathbb C}$, the classical Rudin-Carleson theorem states that there exists a continuous function $F : \overline {\mathbb D} \to {\mathbb C}$ that is holomorphic on ${\mathbb D}$ and satisfies $F\rvert_E = \varphi$. In this talk I will present a generalisation of the Rudin-Carleson theorem for maps into Oka manifolds that additionally includes approximation on compact subsets $K \subset {\mathbb D}$ without any holes and interpolation at a point $c \in {\mathbb D}$. This is joint work in progress with Benedikt Magnússon (University of Iceland).