Anvarjon AhmedovAhmad Fadly Nurullah Rasedee2024-05-282024-05-282015Ahmedov, Anvarjon. On the Weak Localization Principle of the Eigenfunction Expansions of the Laplace-Beltrami Operator By Riesz Method. Institute for Mathematical Research, Universiti Putra Malaysia, 2015.1823-8343https://einspem.upm.edu.my/journal/fullpaper/vol9no2/11.%20ahmad%20fadly.pdfhttps://oarep.usim.edu.my/handle/123456789/5311In 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 Laplace- Beltrami 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.enDistributions; Fourier-laplace series; Laplace-beltrami operator; Localization; Riesz method; SphereArticle33734892