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

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

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Official URL: http://einspem.upm.edu.my/journal/fullpaper/vol9no...

Abstract

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.

Item Type:Article
Keyword:Distributions; Fourier-Laplace series; Localization; Riesz method; Sphere; Laplace-Beltrami operator
Faculty or Institute:Faculty of Engineering
Institute for Mathematical Research
Publisher:Institute for Mathematical Research, Universiti Putra Malaysia
ID Code:38964
Deposited By: Nabilah Mustapa
Deposited On:04 Sep 2015 22:04
Last Modified:04 Sep 2015 22:04

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