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Further Results on the Inverse Base of Axially Monogenic Polynomials

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt

    Mohamed Abdalla

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    Mahmoud Abul-Ez

  3. Department of Mathematics, Faculty of Education for Girls, Tabuk University, Tabuk, Saudi Arabia

    Aida Al-Ahmadi

Authors
  1. Mohamed Abdalla
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  2. Mahmoud Abul-Ez
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  3. Aida Al-Ahmadi
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Correspondence to Mohamed Abdalla.

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Communicated by Ali Hassan Mohamed Murid.

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Abdalla, M., Abul-Ez, M. & Al-Ahmadi, A. Further Results on the Inverse Base of Axially Monogenic Polynomials. Bull. Malays. Math. Sci. Soc. 42, 1369–1381 (2019). https://doi.org/10.1007/s40840-017-0549-x

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  • DOI: https://doi.org/10.1007/s40840-017-0549-x

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