Abstract :
In this paper, we mainly study properties of nullsolutions of the operator Dk (k ∈ N∗ = N \ {0}),
so-called k-regular functions. Firstly, we study the set [P
(0)
p,k] of all homogeneous polynomials of
degree p in x1, . . . , xn which are k-regular in the whole Rn, clearly [P
(0)
p,k] is a right module over
C(Vn,n), we construct a basis [B
(0)
p,k] for the right module [P
(0)
p,k]. 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.
2005 Elsevier Inc. All rights reserved.
