A corresponding Cullen-regularity for split-quaternionic-valued functions

Advances in Difference Equations

Ji Eun Kim¹ 

[1] Department of Mathematics, Dongguk University, Gyeongju-si, Republic of Korea

关键词: split-quaternion;    Cullen’s form;    regular function;    Cauchy-Riemann system;    Clifford analysis;    32A99;    32W50;    30G35;    11E88;   

DOI  :  10.1186/s13662-017-1131-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We give a representation of the class of Cullen-regular functions in split-quaternions. We consider each Cullen’s form of split-quaternions, which provides corresponding Cauchy-Riemann equations for split-quaternionic variables. Using Cullen’s form, we research hyperholomorphy and the properties of functions of split-quaternionic variables which are expressed by hyperbolic coordinates.

【 授权许可】

CC BY