A Phragm\'en - Lindel\"of principle for slice regular functions

TL;DR

This paper extends the classical Phragmen-Lindelof principle to slice regular functions, a class of quaternionic functions, broadening the understanding of maximum modulus principles in hypercomplex analysis.

Contribution

It introduces a Phragmen-Lindelof principle specifically for slice regular functions of quaternionic variables, a recent development in hypercomplex function theory.

Findings

Established a Phragmen-Lindelof principle for slice regular functions.

Extended maximum modulus principles to quaternionic functions.

Contributed to the theory of hypercomplex analysis.

Abstract

The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent papers there has been a resurgence of interest in principles of this type for functions of a hypercomplex variable and for solutions of suitable partial differential equations. In the present article we obtain a Phragmen-Lindelof principle for slice regular functions, a class of quaternion-valued functions of a quaternionic variable which has been recently introduced.