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On the weak localization principle of the eigenfunction expansions of the laplace-beltrami operator by Riesz Method

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On the weak localization principle of the eigenfunction expansions of the laplace-beltrami operator by Riesz Method.pdf (272.43 KB)

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2015

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Universiti Putra Malaysia

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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 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.

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Distributions; Fourier-laplace series; Laplace-beltrami operator; Localization; Riesz method; Sphere

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Ahmedov, 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.

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https://einspem.upm.edu.my/journal/fullpaper/vol9no2/11.%20ahmad%20fadly.pdf
 https://oarep.usim.edu.my/handle/123456789/5311

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