On the sufficient conditions of the localization of the Fourier-Laplace series of distributions from liouville classes

Abstract

Abstract. In this work we investigate the localization principle of the Fourier-Laplace series of the distribution. Here we prove the sufficient conditions of the localization of the Riesz means of the spectral expansions of the Laplace-Beltrami operator on the unit sphere.

The approximation of the solution of wave problems by spectral expansions connected with elliptic differential operators

“…The uniform convergence of the spectral expansions of the distributions connected with the Schrodinger operator is investigated by Ahmedov et al, [10]. We refer the readers to the research by Ahmedov et al, [11] for the results on the convergence of the eigenfunction expansions of the distributions on the unit sphere. The problems on the generalized localization of the spectral expansions of the distributions are considered in the papers by Alimov [12] and Ashurov et al, [13].…”