2005/02/03 by Guy Laville, Ivan Ramadanoff
Mathematics · #math.CV
published as Advances in Clifford algebras 8 (1998) 2, 323-340
arxiv created 2005/02/03 · arxiv updated 2009/12/01
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 = ∑_j=02m+1 e_j ∂\over ∂ x_j be the usual operator for monogenic functions and Δ the ordinary Laplacian. The holomorphic Cliffordian functions are functions f : \R2m+2 \fle \R_0,2m+1, which are solutions of D Δm f = 0