Resumen de Extensions of bounded holomorphic functions on the tridisk

Lukasz Kosinski, John E. McCarthy

• A set V in the tridisk D3 has the polynomial extension property if for every polynomial p there is a function ϕ on D3 so that ∥ϕ∥D3=∥p∥V and ϕ|V=p|V. We study sets V that are relatively polynomially convex and have the polynomial extension property. If V is one-dimensional, and is either algebraic, or has polynomially convex projections, we show that it is a retract. If V is two-dimensional, we show that either it is a retract, or, for any choice of the coordinate functions, it is the graph of a function of two variables.