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On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method

In this paper we deal with the problems of the weak localization of the eigenfunction expansions related to Laplace-Beltrami operator on unit sphere. The conditions for weak localization of Fourier-Laplace series are investigated by comparing the Riesz and Cesaro methods of summation for eigenfunct...

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Main Authors: Ahmedov, Anvarjon, Rasedee, Ahmad Fadly Nurullah
Format: Article
Language:English
Published: Institute for Mathematical Research, Universiti Putra Malaysia 2015
Online Access:http://psasir.upm.edu.my/id/eprint/38964/1/38964.pdf
http://psasir.upm.edu.my/id/eprint/38964/
http://einspem.upm.edu.my/journal/fullpaper/vol9no2/11.%20ahmad%20fadly.pdf
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spelling my.upm.eprints.389642015-09-04T14:04:10Z http://psasir.upm.edu.my/id/eprint/38964/ On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method Ahmedov, Anvarjon Rasedee, Ahmad Fadly Nurullah In this paper we deal with the problems of the weak localization of the eigenfunction expansions related to Laplace-Beltrami operator on unit sphere. The conditions for weak localization of Fourier-Laplace series are investigated by comparing the Riesz and Cesaro methods of summation for eigenfunction expansions of the LaplaceBeltrami operator. It is shown that the weak localization principle for the integrable functions f (x) at the point x depends not only on behavior of the function around x but on the behavior of the function around diametrically opposite point x. Institute for Mathematical Research, Universiti Putra Malaysia 2015-05 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/38964/1/38964.pdf Ahmedov, Anvarjon and Rasedee, Ahmad Fadly Nurullah (2015) On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method. Malaysian Journal of Mathematical Sciences, 9 (2). pp. 337-348. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol9no2/11.%20ahmad%20fadly.pdf
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 In this paper we deal with the problems of the weak localization of the eigenfunction expansions related to Laplace-Beltrami operator on unit sphere. The conditions for weak localization of Fourier-Laplace series are investigated by comparing the Riesz and Cesaro methods of summation for eigenfunction expansions of the LaplaceBeltrami operator. It is shown that the weak localization principle for the integrable functions f (x) at the point x depends not only on behavior of the function around x but on the behavior of the function around diametrically opposite point x.
format Article
author Ahmedov, Anvarjon
Rasedee, Ahmad Fadly Nurullah
spellingShingle Ahmedov, Anvarjon
Rasedee, Ahmad Fadly Nurullah
On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method
author_facet Ahmedov, Anvarjon
Rasedee, Ahmad Fadly Nurullah
author_sort Ahmedov, Anvarjon
title On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method
title_short On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method
title_full On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method
title_fullStr On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method
title_full_unstemmed On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method
title_sort on the weak localization principle of the eigenfunction expansions of the laplace-beltrami operator by riesz method
publisher Institute for Mathematical Research, Universiti Putra Malaysia
publishDate 2015
url http://psasir.upm.edu.my/id/eprint/38964/1/38964.pdf
http://psasir.upm.edu.my/id/eprint/38964/
http://einspem.upm.edu.my/journal/fullpaper/vol9no2/11.%20ahmad%20fadly.pdf
_version_ 1643832285701603328
score 13.18916

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