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

TL;DR

This paper extends the Menchov-Trokhimchuk theorem to broader classes of monogenic functions in three-dimensional commutative algebra subspaces, relaxing the conditions for their monogenity.

Contribution

It introduces a generalized version of the theorem for monogenic functions in specific algebraic subspaces, reducing the restrictions needed for monogenity.

Findings

Weakened conditions for monogenity in three-dimensional commutative algebra subspaces.

Established new criteria linking continuity and Gato derivative for monogenic functions.

Extended classical theorem to broader algebraic contexts.

Abstract

The aim of this work is to weaken the conditions of monogenity for functions that take values in subspaces of 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.