A generalization of the classical Rudin-Carleson extension theorem from the unit disc to any k-connected bounded domain (k>1) whose boundary is k disjoint Jordan curves: every continuous function on a closed arclength-null boundary set, obeying a continuous pointwise bound, extends to a function continuous on the closure and holomorphic inside that meets the bound on the boundary and additionally interpolates prescribed values at finitely many interior points. The proof introduces and relies on an annular version of the F. and M. Riesz theorem, following Bishop's characterization of extendability sets.
A complex-analysis paper generalizing the Rudin-Carleson theorem from the unit disc to finitely (multiply) connected bounded domains. The classical theorem says a continuous function on an arclength-…