Abstract
The paper first discusses several regularity conditions of functions of a 2N-dimensional hypercomplex variable, each of which is defined on different subspace of the 2N-dimensional space. The power-associative law is assumed but not the associative or the alternative laws for the algebra. Some such regular functions are then constructed: a set of regular functions are constructed from functions of a complex variable; polynomial and exponential functions are constructed using the generating function. The Fourier representation of the regular function is briefly discussed. Some analysis obtained for the associative case does carry over to the nonassociative and nonalternative cases. The results of this paper apply to functions of a Clifford variable as well as that of a Cayley- Dickson variable.
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