On the convergence of the Cesaro Mean of the Fourier-Laplace serieas

• Main Author: Rakhimov, Abdumalik
• Format: Article
• Language: English
• Published: SANDKRS sdn bhd. 2023
• Subjects: QA300 Analysis
• Online Access: http://irep.iium.edu.my/106307/7/106307_On%20the%20convergence%20of%20the%20Cesaro%20Mean.pdf; http://irep.iium.edu.my/106307/; https://www.jcscm.net/cms/?action=showissue&volume=13&issue=2
• Institution: Universiti Islam Antarabangsa Malaysia

Objectives of this paper are to study convergence and summability of the Fourier-Laplace series in the spaces of singular distributions. The Cezaro means employed for summation of these series and estimations of the spectral function in the Sobolev spaces for this study. In this we employ embedding thoren in connection with the fractional powers of the Laplace operator on a sphere. It is established exact relations between singularity and order of the means which are sufficient for the convergence and summability. Findings of the paper can be used in the solutions of the problems of engineering and mathematical physics such as heat transfer and/or wave propagations on in the surfaces by the series methods in eigen�function expansions associated with the differential operators de�fined on the surfaces.