Determining sets for holomorphic functions on the symmetrized bidisk

TL;DR

This paper investigates the properties of determining sets for holomorphic functions on the symmetrized bidisk, linking them to Nevanlinna-Pick interpolation and the conditions under which thin sets are determining.

Contribution

It introduces new criteria for determining sets in the symmetrized bidisk and explores their relation to interpolation problems and thin sets.

Findings

Characterization of determining sets for holomorphic functions on the symmetrized bidisk

Connection between determining sets and Nevanlinna-Pick interpolation solutions

Conditions under which thin sets are determining

Abstract

This paper studies the determining sets for analytic functions from the symmetrized bidisk into the open unit disk in $\mathbb C$. It relates the idea to the uniqueness of the solutions of a Nevanlinna-Pick interpolation problem. It also investigates when certain thin sets can be determining.