Absence of localization of the Laplace series on the sphere for functions of the Nikol'skii class $H_1^1(S^2)$

In this article a function is constructed belonging to the class $H_1^1(S^2)$ and having a singularity at a definite point on the sphere, as a consequence of which localization fails for the Laplace series of this function at the diametrically opposite point. The constructed example shows that the sufficient condition of localization in $H_p^a$ of the spectral expansions in the class of all elliptic differential operators on an $n$-dimensional paracompact manifold cannot be improved (see [1]).