International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 8, Issue 11 (November 2021), Pages: 1-9

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 Original Research Paper

 Title: Analysis of Gegenbauer kernel filtration on the hypersphere

 Author(s): Louis Omenyi 1, *, McSylvester Omaba 2, Emmanuel Nwaeze 1, Michael Uchenna 1

 Affiliation(s):

 1Department of Mathematics and Statistics, Alex Ekwueme Federal University, Ndufu-Alike, Nigeria
 2Department of Mathematics, College of Science, University of Hafr Al Batin, Hafr Al Batin, Saudi Arabia

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-8628-0298

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2021.11.001

 Abstract:

In this study, we aim to construct explicit forms of convolution formulae for Gegenbauer kernel filtration on the surface of the unit hypersphere. Using the properties of Gegenbauer polynomials, we reformulated Gegenbauer filtration as the limit of a sequence of finite linear combinations of hyperspherical Legendre harmonics and gave proof for the completeness of the associated series. We also proved the existence of a fundamental solution of the spherical Laplace-Beltrami operator on the hypersphere using the filtration kernel. An application of the filtration on a one-dimensional Cauchy wave problem was also demonstrated. 

 © 2021 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Spherical Laplacian, Hypersphere, Gegenbauer kernel, Filtration, Cauchy wave problem

 Article History: Received 28 May 2021, Received in revised form 10 August 2021, Accepted 25 August 2021

 Acknowledgment 

The first author thanks the leadership and members of the Seminar and Research Committee of the Department of Mathematics and Statistics of the Alex Ekwueme Federal University, Ndufu-Alike for their valuable scientific discussions that facilitated the completion of this research. All the authors express sincere gratitude to their family members for providing the support to work.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Omenyi L, Omaba M, and Nwaeze E et al. (2021). Analysis of Gegenbauer kernel filtration on the hypersphere. International Journal of Advanced and Applied Sciences, 8(11): 1-9

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 Figures

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