An extension theorem for regular functions of two quaternionic variables

TL;DR

This paper extends the theory of regular functions of two quaternionic variables by establishing a boundary propagation theorem, similar to classical results in complex analysis, for Fueter-regular functions.

Contribution

It introduces a new extension theorem for Fueter-regular functions of two quaternionic variables, expanding the understanding of boundary behavior and extendability.

Findings

Ball in boundary propagates regular extendability

Establishes a quaternionic analogue of Hanges and Trèves theorem

Enhances boundary regularity theory for quaternionic functions

Abstract

For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves theorem. Namely, we show that a ball contained in the boundary of a domain is a propagator of regular extendability across the boundary.