Properties of Regular Functions With Values in Bicomplex Numbers

Abstract

Abstract. In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

Conformal Numbers

“…One of the possible generalizations with potentially underestimated relevance in physics is the bicomplex number system [1,2,3,4,5]. Recent investigations in this area have been provided for example by [6,7,8,9,10]. The number system is also known under the name of Segre numbers [11].…”

The corresponding inverse of functions of multidual complex variables in Clifford analysis

“…Kim and Shon [11,12] investigated properties of a corresponding Cauchy-Riemann system and a regularity of functions with values in special quaternions defined by the corresponding differential operators of special quaternions systems. Kim and Shon [13] investigated the differentiation and integration for regular functions of bicomplex numbers satisfying the commutative multiplicative rule.…”

A regularity of split-biquaternionic-valued functions in Clifford analysis

“…[4,7] obtained some results regarding the regularity of functions on the reduced quaternion field, and on the form of (dual) split quaternions, defined by differential operators in Clifford analysis. In addition, Kim and Shon [5,6] researched corresponding Cauchy-Riemann systems and the properties of functions with values in special quaternions (such as reduced or split-quaternions) by using a regular function with values in dual split-quaternions and gave properties and calculations of functions of bicomplex variables with the commutative multiplication rule [8]. Kim [3] studied the corresponding inverse of functions of multidual complex variables in Clifford analysis.…”