Basic Sets of Special Monogenic Polynomials in Fréchet Modules. (14th February 2017)

• Record Type: Journal Article
• Authors: Farghaly Hassan, Gamal; Aloui, Lassaad; Bakali, Allal
• Other Names: Dyakonov Konstantin M. Academic Editor.
• Is Part Of: Journal of complex analysis. Volume 2017(2017)
• Publication Date: 2017-02-14
• Subjects: Functions of complex variables -- Periodicals; Mathematical analysis -- Periodicals; 515.905
• DOI: 10.1155/2017/2075938
• Languages: English
• ISSNs: 2314-4963

Abstract

Abstract : 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.