A set in the tridisk has the polynomial extension property if for every polynomial there is a function on so that and . We study sets that are relatively polynomially convex and have the polynomial extension property. If is one-dimensional, and is either algebraic, or has polynomially convex projections, we show that it is a retract. If 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.
Cite this article
Łukasz Kosiński, John E. McCarthy, Extensions of bounded holomorphic functions on the tridisk. Rev. Mat. Iberoam. 36 (2020), no. 3, pp. 791–816DOI 10.4171/RMI/1149