Table of Contents
Journal of Complex Analysis
Volume 2017, Article ID 2075938, 11 pages
Research Article

Basic Sets of Special Monogenic Polynomials in Fréchet Modules

1Department of Mathematics, Faculty of Sciences, Northern Border University, P.O. Box 1321, Arar, Saudi Arabia
2Faculty of Science, University of Assiut, Assiut 71516, Egypt
3Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis-El Manar, Tunis, Tunisia

Correspondence should be addressed to Gamal Farghaly Hassan; moc.oohay@wen6lamag

Received 20 June 2016; Revised 31 October 2016; Accepted 18 December 2016; Published 14 February 2017

Academic Editor: Konstantin M. Dyakonov

Copyright © 2017 Gamal Farghaly Hassan et al. 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.


This article is concerned with the study of the theory of basic sets in Fréchet modules in Clifford analysis. The main aim of this account, which is based on functional analysis consideration, is to formulate criteria of general type for the effectiveness (convergence properties) of basic sets either in the space itself or in a subspace of finer topology. By attributing particular forms for the Fréchet module of different classes of functions, conditions are derived from the general criteria for the convergence properties in open and closed balls. Our results improve and generalize some known results in complex and Clifford setting concerning the effectiveness of basic sets.