Analog of Menchov-Trokhimchuk theorem for monogenic functions in three-dimensional commutative algebra

TL;DR

This paper extends the Menchov-Trokhimchuk theorem to monogenic functions in three-dimensional commutative algebras, relaxing the conditions needed for monogenity based on continuity and Gato derivative existence.

Contribution

It generalizes the theorem for monogenic functions in three-dimensional commutative algebras, weakening the conditions required for monogenity.

Findings

Established weaker conditions for monogenity in three-dimensional commutative algebras.

Connected monogenity with continuity and Gato derivative existence.

Extended classical theorem to a broader class of algebra-valued functions.

Abstract

The aim of this work is to weaken the conditions of monogenity for functions that take values in one concrete three-dimensional commutative algebras over the field of complex numbers. The monogenity of the function understood as a combination of its continuity with the existence of a Gato derivative.