Universality of Automorphisms on the Ball of Bounded Holomorphic Functions on the Polydisk

TL;DR

This paper investigates the conditions under which automorphisms of the polydisk induce universal inner functions on the space of bounded holomorphic functions, revealing a new connection between automorphism sequences and function universality.

Contribution

It establishes a criterion linking automorphism sequences of the polydisk to the existence of universal inner functions in the associated function space.

Findings

Automorphism sequences can generate universal inner functions under specific conditions.

A new criterion for universality based on automorphism properties is proposed.

The results connect geometric automorphism behavior with functional universality.

Abstract

Given a sequence of automorphisms of the polydisk, we show that the associated composition semigroup homomorphisms on the ball of bounded holomorphic functions on the polydisk admit a universal inner function if a certain condition on the automorphisms are satisfied.