Holomorphic Cliffordian functions |
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Authors: | Guy Laville Ivan Ramadanoff |
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Institution: | (1) UPRES-A 6081 Département de Mathématiques, Université de Caen, 14032 Caen Cedex, France |
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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, 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. |
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Keywords: | |
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