On k-regular functions with values in a universal Clifford algebra

In this paper, we mainly study properties of nullsolutions of the operator D-k (k is an element of N* = N \ {0}), so-called k-regular functions. Firstly, we study the set [P-p,k((0))] of all homogeneous polynormals of degree p in x1,...,x(n) which are k-regular in the whole R-n, clearly [P-p,k((0))] is a right module over C(V-n,V-n), we construct a basis [B-p,k((0))] for the right module [P-p,k((0))]. Secondly, we study the k-regular and analytic functions, and we give the Taylor expansions for these functions. At last, the corresponding Taylor expansions for k-regular functions are given since each k-regular function is a real analytic function. (c) 2005 Elsevier Inc. All rights reserved.