The Regularity of Functions on Dual Split Quaternions in Clifford Analysis

Abstract

This paper shows some properties of dual split quaternion numbers and expressions of power series in dual split quaternions and provides differential operators in dual split quaternions and a dual split regular function on $\mathrm{\Omega }\subset {ℂ}^2\times {ℂ}^2$ that has a dual split Cauchy-Riemann system in dual split quaternions.