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- W2034172983 abstract "The aim of this paper is to put the foundations of a new theory of functions, called holomorphic Cliffordian, which should play an essential role in the generalization of holomorphic functions to higher dimensions. Let ℝ0,2m+1 be the Clifford algebra of ℝ2m+1 with a quadratic form of negative signature, $$D = sumlimits_{j = 0}^{2m + 1} {e_j {partial over {partial x_j }}} $$ be the usual operator for monogenic functions and Δ the ordinary Laplacian. The holomorphic Cliffordian functions are functionsf: ℝ2m+2 → ℝ0,2m+1, which are solutions ofDδ m f = 0. Here, we will study polynomial and singular solutions of this equation, we will obtain integral representation formulas and deduce the analogous of the Taylor and Laurent expansions for holomorphic Cliffordian functions. In a following paper, we will put the foundations of the Cliffordian elliptic function theory." @default.
- W2034172983 created "2016-06-24" @default.
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- W2034172983 date "1998-12-01" @default.
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- W2034172983 title "Holomorphic Cliffordian functions" @default.
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- W2034172983 doi "https://doi.org/10.1007/bf03043103" @default.
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