On monogenic functions defined in different commutative algebras

TL;DR

This paper explores the relationship between monogenic functions in various finite-dimensional commutative algebras, establishing a correspondence that simplifies their study by relating them to functions in a specific algebra.

Contribution

It introduces a novel correspondence linking monogenic functions across different commutative algebras, aiding in their analysis and classification.

Findings

Established a correspondence between monogenic functions in different algebras

Reduced the study of monogenic functions to a special algebra case

Facilitated understanding of monogenic functions through algebraic relationships

Abstract

A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.