Schur-Agler class rational inner functions on the tridisk

Abstract

We prove two results with regard to rational inner functions in the Schur-Agler class of the tridisk. Every rational inner function of degree ( n , 1 , 1 ) (n,1,1) is in the Schur-Agler class, and every rational inner function of degree ( n , m , 1 ) (n,m,1) is in the Schur-Agler class after multiplication by a monomial of sufficiently high degree.