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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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38964/ http://psasir.upm.edu.my/id/eprint/38964/1/38964.pdf |
| _version_ | 1848849017087197184 |
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| author | Ahmedov, Anvarjon Rasedee, Ahmad Fadly Nurullah |
| author_facet | Ahmedov, Anvarjon Rasedee, Ahmad Fadly Nurullah |
| author_sort | Ahmedov, Anvarjon |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T09:43:42Z |
| format | Article |
| id | upm-38964 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:43:42Z |
| publishDate | 2015 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| spellingShingle | Ahmedov, Anvarjon Rasedee, Ahmad Fadly Nurullah On the weak localization principle of the eigenfunction expansions of the Laplace-Beltrami operator by Riesz method |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/38964/ http://psasir.upm.edu.my/id/eprint/38964/ http://psasir.upm.edu.my/id/eprint/38964/1/38964.pdf |