Rational penta-inner functions and the distinguished boundary of the pentablock

TL;DR

This paper characterizes rational functions from the unit disc to the pentablock that map boundary to boundary, providing a new description of the pentablock's distinguished boundary.

Contribution

It introduces a novel characterization of the distinguished boundary of the pentablock and describes rational maps with boundary-preserving properties.

Findings

New description of the distinguished boundary of the pentablock

Characterization of boundary-preserving rational maps from the disc to the pentablock

Insights into the structure of rational penta-inner functions

Abstract

In this note, we give a description of rational maps from the open unit disc $\mathbb{D}$ to the pentablock that map the boundary of $\mathbb{D}$ to the distinguished boundary of the pentablock. We also obtain a new characterization of the distinguished boundary of the pentablock.