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- W2082023197 abstract "A system of multidimensional complex numbers and variables is developed, with emphasis on three dimensions. The algebra of the system is commutative in multiplication, but is not a “division algebra.” The system is therefore fundamentally different from quaternions, whose algebra is not commutative in multiplication, but is a division algebra. The three-dimensional (3-D) system is a direct analog of the ordinary two-dimensional system of complex numbers and variables. With this algebra, functions of a 3-D variable are defined, and significant elements of a theory of analytic functions of one 3-D variable are developed, including conditions of analyticity analogous to the Cauchy–Riemann conditions. It is shown how the parts of a 3-D function provide components of solenoidal and irrotational harmonic vectors in three dimensions. The theoretical foundation developed here is to be further developed and applied in subsequent papers." @default.
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- W2082023197 date "1989-01-01" @default.
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- W2082023197 title "Some elements of a theory of multidimensional complex variables: part I. general theory" @default.
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- W2082023197 doi "https://doi.org/10.1016/0016-0032(89)90024-0" @default.
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