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
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.