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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Bibliographic Details
Published inJournal of physics. Conference series Vol. 890; no. 1; pp. 12117 - 12123
Main Authors Nurullah Rasedee, Ahmad Fadly, Ahmedov, Anvarjon, Abdul Sathar, Mohammad Hasan
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.09.2017
Subjects
Asymptotic properties
Convergence
Fourier series
Heat transfer
Kernels
Mass transfer
Mathematical analysis
Mathematical models
Operators (mathematics)
Physics
Spectra
Sums
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/890/1/012117