Regular Functions with Values in Ternary Number System on the Complex Clifford Analysis

Abstract

We define a new modified basis $\widehat{i}$ which is an association of two bases, $e_1$ and $e_2$. We give an expression of the form $z=x_0+ \widehat{i }\stackrel{-}{z_0}$, where $x_0$ is a real number and $\stackrel{-}{z_0}$ is a complex number on three-dimensional real skew field. And we research the properties of regular functions with values in ternary field and reduced quaternions by Clifford analysis.