On the generalized continuity of a function at the points of convergence of its spectral decomposition

In this paper, we study the necessary conditions for the summability of spectral expansions in eigenfunctions of the Schr¨odinger operator with a singular potential on an arbitrary N− dimensional domain. It is proved that if the spectral expansion of an arbitrary function at some point is summed by Riesz means, then its mean value over the sphere at the specified point has generalized continuity.