Beurling-Lax type theorems in the complex and quaternionic setting: the half-space case

TL;DR

This paper generalizes the Beurling-Lax theorem to complex and quaternionic settings, encompassing meromorphic and slice hypermeromorphic functions in half-space domains, and unifies various classical function spaces.

Contribution

It introduces a unified framework for Beurling-Lax theorems applicable to both complex and quaternionic half-space domains, extending classical results to broader function classes.

Findings

Generalization of Beurling-Lax theorem to meromorphic functions in half-planes

Extension to slice hypermeromorphic functions in quaternionic half-space

Unified framework covering disk and half-space domains

Abstract

We give a generalization of the Beurling-Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.