International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 11, Pages 717-726
doi:10.1155/S0161171203201083

On the convergence properties of basic series representing Clifford valued functions

M. A. Abul-Ez1 and D. Constales2

 1Department of Mathematics, Faculty of Science, South Valley University, Sohag 82524, Egypt
2Department of Mathematical Analysis, Ghent University, Galglaan 2 Ghent, Ghent B-9000, Belgium
Received 21 January 2002

Abstract

It is shown that certain classes of special monogenic functions cannot be represented by the basic series in the whole space. New definitions for the order of basis of special monogenic polynomials are given, together with theorems on the representation of classes of special monogenic functions in certain balls and at a point.