Affiliation:
1. Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2. Faculty of Science, University of Assiut, Assiut 71516, Egypt
Abstract
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.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference33 articles.
1. The uniqueness of expansion in polynomials;Whittaker;J. Lond. Math. Soc.,1935
2. Whittaker, J.M., and Gattegno, C. (1949). Sur les Séries de Base de Polynbmes Quelconques, Gauthier-Villars.
3. On the convergence of series of polynomials;Cannon;Proc. Lond. Math. Soc.,1937
4. On the representation of integral functions by general basic series;Cannon;Math. Z.,1939
5. Boas, R.P., and Buck, R.B. (1964). Polynomial Expansions of Analytic Functions, Springer Science & Business Media.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献