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Regular functions with values in ternary number system on the complex Clifford analysis. (English) Zbl 1295.30113

Summary: We define a new modified basis \(\hat{i}\) which is an association of two bases, \(e_1\) and \(e_2\). We give an expression of the form \(z=x_0+\hat{i}\overline{z_0}\), where \(x_0\) is a real number and \(\overline{z_0}\) 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.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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