On the representation of monogenic functions by the product bases of polynomials

Abul-Ez, Mahmoud; Abdalla, Mohamed; Al-Ahmadi, Aidah

doi:10.2298/fil2004209a

Cited by 2 publications

(1 citation statement)

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“…It is not very surprising that the product of two effective bases does not maintain effectiveness, as shown in [19], where the authors studied the effectiveness of the product of simple bases. Recently, in [20], a generalization of the product base for functions with bounded radii of convergence was investigated. The inverse of an effective base does not need to be effective [21].…”

Section: Introductionmentioning

confidence: 99%

Equivalent Base Expansions in the Space of Cliffordian Functions

Zayed

Hassan

2023

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Intensive research efforts have been dedicated to the extension and development of essential aspects that resulted in the theory of one complex variable for higher-dimensional spaces. Clifford analysis was created several decades ago to provide an elegant and powerful generalization of complex analyses. In this paper, first, we derive a new base of special monogenic polynomials (SMPs) in Fréchet–Cliffordian modules, named the equivalent base, and examine its convergence properties for several cases according to certain conditions applied to related constituent bases. Subsequently, we characterize its effectiveness in various convergence regions, such as closed balls, open balls, at the origin, and for all entire special monogenic functions (SMFs). Moreover, the upper and lower bounds of the order of the equivalent base are determined and proved to be attainable. This work improves and generalizes several existing results in the complex and Clifford context involving the convergence properties of the product and similar bases.

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Section: Introductionmentioning

confidence: 99%