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Regularity of Functions on the Reduced Quaternion Field in Clifford Analysis

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  • Ji Eun Kim
  • Su Jin Lim
  • Kwang Ho Shon

Abstract

We define a new hypercomplex structure of ℝ3 and a regular function with values in that structure. From the properties of regular functions, we research the exponential function on the reduced quaternion field and represent the corresponding Cauchy‐Riemann equations in hypercomplex structures of ℝ3.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:654798
DOI: 10.1155/2014/654798
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