Slice regular functions in several variables

TL;DR

This paper develops a foundational theory of slice regular functions in multiple variables over various real alternative $^*$-algebras, extending classical holomorphic function theory to broader algebraic contexts.

Contribution

It introduces the first comprehensive framework for slice regular functions in several variables over diverse algebraic structures like quaternions, octonions, and Clifford algebras.

Findings

Established foundational properties of slice regular functions in multiple variables.

Extended classical holomorphic function theory to real alternative $^*$-algebras.

Provided a basis for further research in hypercomplex analysis.

Abstract

In this paper, we lay the foundations of the theory of slice regular functions in several variables ranging in any real alternative $^*$-algebra, including quaternions, octonions and Clifford algebras. This theory is an extension of the classical theory of holomorphic functions in several complex variables.