International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 11, Pages 717-726

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

Copyright © 2003 M. A. Abul-Ez and D. Constales. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.