Basic sets of polynomials in Clifford analysis. (English) Zbl 0663.41009

Abul-Ez, M. A.; Constales, D.

Complex Variables, Theory Appl. 14, No. 1-4, 177-185 (1990).

This paper is concerned with the extension of the theory of basic sets of polynomials in one complex variable, as introduced by J. M. Whittaker and B. Cannon, to the setting of Clifford analysis. This is the natural generalization of complex analysis to Euclidean space of dimension larger than two, where the regular functions have values in a Clifford algebra and are null-solutions of a linear differential operator which linearizes the laplacian. An important subclass of the Clifford regular functions are considered, for which a Cannon theorem on the effectiveness in closed balls is proved. This result is consequently refined in terms of the order and type of entire functions in this subclass.

Reviewer: M.A.Abul-Ez

MSC:

41A10	Approximation by polynomials
30G35	Functions of hypercomplex variables and generalized variables

Keywords:

Cannon sum of basic sets; effectiveness; monogenic functions; basic sets of polynomials; Clifford analysis