Holomorphic Cliffordian Functions
Abstract
The aim of this paper is to put the fundations 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 R\0,2m+1 be the Clifford algebra of R2m+1 with a quadratic form of negative signature, D = Σ\j=02m+1 e\j ∂ ∂ x\j be the usual operator for monogenic functions and the ordinary Laplacian. The holomorphic Cliffordian functions are functions f : 2m+2 \0,2m+1, which are solutions of D m f = 0
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