On the approximation of the function on the unite sphere by the spherical harmonics
Keywords:
Approximation, Fourier series on a sphere, Summability, Functions Spaces, DistributionsAbstract
In this paper we discuss convergence and summability of the Fourier series of distributions in the domains where it coincides with smooth functions in eigenfunction expansions of the Laplace operator on the unite sphere. We consider representation of the distributions defined on the unit sphere by its Fourier-Laplace series by the spherical harmonics in different topologies. Mainly we study the Chesaro method of summation such a series
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