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Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere

The mathematical models of the heat and mass transfer processes on the ball type solids can be solved using the theory of convergence of Fourier-Laplace series on unit sphere. Many interesting models have divergent Fourier-Laplace series, which can be made convergent by introducing Riesz and Cesaro...

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Main Authors: Rasedee, Ahmad Fadly Nurullah, Ahatjonovich, Anvarjon Ahmedov, Abdul Sathar, Mohammad Hasan
Format: Article
Language:English
Published: Institute of Physics Publishing 2017
Online Access:http://psasir.upm.edu.my/id/eprint/60967/1/Asymptotic%20formula%20for%20the%20Riesz%20means%20of%20the%20spectral%20functions%20of%20Laplace-Beltrami%20operator%20on%20unit%20sphere.pdf
http://psasir.upm.edu.my/id/eprint/60967/
https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012117/pdf
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spelling my.upm.eprints.609672019-03-21T04:59:12Z http://psasir.upm.edu.my/id/eprint/60967/ Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere Rasedee, Ahmad Fadly Nurullah Ahatjonovich, Anvarjon Ahmedov Abdul Sathar, Mohammad Hasan The mathematical models of the heat and mass transfer processes on the ball type solids can be solved using the theory of convergence of Fourier-Laplace series on unit sphere. Many interesting models have divergent Fourier-Laplace series, which can be made convergent by introducing Riesz and Cesaro means of the series. Partial sums of the Fourier-Laplace series summed by Riesz method are integral operators with the kernel known as Riesz means of the spectral function. In order to obtain the convergence results for the partial sums by Riesz means we need to know an asymptotic behavior of the latter kernel. In this work the estimations for Riesz means of spectral function of Laplace-Beltrami operator which guarantees the convergence of the Fourier-Laplace series by Riesz method are obtained. Institute of Physics Publishing 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/60967/1/Asymptotic%20formula%20for%20the%20Riesz%20means%20of%20the%20spectral%20functions%20of%20Laplace-Beltrami%20operator%20on%20unit%20sphere.pdf Rasedee, Ahmad Fadly Nurullah and Ahatjonovich, Anvarjon Ahmedov and Abdul Sathar, Mohammad Hasan (2017) Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere. Journal of Physics: Conference Series, 890 (1). pp. 1-7. ISSN 1742-6588; ESSN: 1742-6596 https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012117/pdf 10.1088/1742-6596/890/1/012117
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description The mathematical models of the heat and mass transfer processes on the ball type solids can be solved using the theory of convergence of Fourier-Laplace series on unit sphere. Many interesting models have divergent Fourier-Laplace series, which can be made convergent by introducing Riesz and Cesaro means of the series. Partial sums of the Fourier-Laplace series summed by Riesz method are integral operators with the kernel known as Riesz means of the spectral function. In order to obtain the convergence results for the partial sums by Riesz means we need to know an asymptotic behavior of the latter kernel. In this work the estimations for Riesz means of spectral function of Laplace-Beltrami operator which guarantees the convergence of the Fourier-Laplace series by Riesz method are obtained.
format Article
author Rasedee, Ahmad Fadly Nurullah
Ahatjonovich, Anvarjon Ahmedov
Abdul Sathar, Mohammad Hasan
spellingShingle Rasedee, Ahmad Fadly Nurullah
Ahatjonovich, Anvarjon Ahmedov
Abdul Sathar, Mohammad Hasan
Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere
author_facet Rasedee, Ahmad Fadly Nurullah
Ahatjonovich, Anvarjon Ahmedov
Abdul Sathar, Mohammad Hasan
author_sort Rasedee, Ahmad Fadly Nurullah
title Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere
title_short Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere
title_full Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere
title_fullStr Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere
title_full_unstemmed Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere
title_sort asymptotic formula for the riesz means of the spectral functions of laplace-beltrami operator on unit sphere
publisher Institute of Physics Publishing
publishDate 2017
url http://psasir.upm.edu.my/id/eprint/60967/1/Asymptotic%20formula%20for%20the%20Riesz%20means%20of%20the%20spectral%20functions%20of%20Laplace-Beltrami%20operator%20on%20unit%20sphere.pdf
http://psasir.upm.edu.my/id/eprint/60967/
https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012117/pdf
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score 13.211869

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