Determining sets for holomorphic functions on the symmetrized bidisk

Abstract

A subset D of a domain omega c C-d is determining for an analytic function f : omega-+ D if whenever an analytic function g : omega-+ D coincides with f on D, equals to f on whole omega. This note finds several sufficient conditions for a subset of the symmetrized bidisk to be determining. For any N >_ 1, a set consisting of N-2 -N + 1 many points is constructed which is determining for any rational inner function with a degree constraint. We also investigate when the intersection of the symmetrized bidisk intersected with some special algebraic varieties can be determining for rational inner functions