Schur-Agler class rational inner functions on the tridisk

TL;DR

This paper investigates rational inner functions on the tridisk, establishing their inclusion in the Schur-Agler class under specific degree conditions, thereby advancing understanding of their structural properties.

Contribution

It proves that rational inner functions of certain degrees are in the Schur-Agler class, including those that require multiplication by a high-degree monomial.

Findings

Rational inner functions of degree (n,1,1) are in the Schur-Agler class.

Rational inner functions of degree (n,m,1) become in the class after multiplication by a high-degree monomial.

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) is in the Schur-Agler class, and every rational inner function of degree (n,m,1) is in the Schur-Agler class after multiplication by a monomial of sufficiently high degree.