KASS seminar

Abstract: We will discuss ongoing work on a generalization of Runge's theorem for approximation with members of proper subrings of the polynomials. The subrings in question consist of polynomials whose exponents are restricted to some cone. A similar result to Runge's theorem can be obtained if polynomial convexity is replaced by convexity with respect to the ring one wants to approximate from. In particular, sharp results can be obtained when the domain of the function is Reinhardt.