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Further Results on the Inverse Base of Axially Monogenic Polynomials

  • Mohamed AbdallaEmail author
  • Mahmoud Abul-Ez
  • Aida Al-Ahmadi
Article

Abstract

The main goal of this paper is to investigate the convergence properties of the inverse base of axially monogenic polynomials. These convergence properties proceed from the investigation of the relation between the effectiveness in closed balls, open balls as well as effectiveness for integral functions. The obtained results are the natural generalization of the original ones in complex setting to higher dimensions. In the meantime our results cover some open questions concerning the Clifford inverse bases.

Keywords

Axially monogenic function Bases of polynomials Inverse base Convergence properties 

Mathematics Subject Classification

30G35 41A10 

Notes

Acknowledgements

The authors are very grateful to the anonymous referees for many valuable comments and suggestions which helped to improve the paper.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  • Mohamed Abdalla
    • 1
    Email author
  • Mahmoud Abul-Ez
    • 2
  • Aida Al-Ahmadi
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceSouth Valley UniversityQenaEgypt
  2. 2.Department of Mathematics, Faculty of ScienceSohag UniversitySohagEgypt
  3. 3.Department of Mathematics, Faculty of Education for GirlsTabuk UniversityTabukSaudi Arabia

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