A corresponding Cullen-regularity for split-quaternionic-valued functions. (English) Zbl 1422.30071
Summary: 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.
MSC:
| 30G30 | Other generalizations of analytic functions (including abstract-valued functions) |
| 15A66 | Clifford algebras, spinors |
Keywords:
split-quaternion; Cullen’s form; regular function; Cauchy-Riemann system; Clifford analysisReferences:
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