Hausdorff analytic functions in a three-dimensional associative noncommutative algebra

Abstract

A class of H-analytic (differentiable by Hausdorff) functions in a three-dimensional noncommutative algebra $\mathbb{\widetilde{A}}_{2}$ over the field $\mathbb{C}$ is considered. All $H$-analytic functions are described in the explicit form. The obtained description is applied to the integral representation of these functions, and the mentioned functions are also applied when solving some PDEs.