ON THE APPROXIMATION OF THE FUNCTION ON THE UNIT SPHERE BY THE SPHERICAL HARMONICS
DOI:
https://doi.org/10.46754/jmsi.2023.12.004Keywords:
Approximation, Fourier series on a sphere, Summability, Functions Spaces, DistributionsAbstract
In this paper, the convergence and summability of the Fourier series for distributions in domains coinciding with smooth functions in eigenfunction expansions of the Laplace operator on the unite sphere are explored. The representation of distributions defined on the unit sphere by their Fourier-Laplace series, employing spherical harmonics in different topologies, is examined. The main focus lies in studying the Cesaro method for summing such a series.
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