Geodesic
Absence of localization of the Laplace series on the sphere for functions of the Nikol'skii class $H_1^1(S^2)$
Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 517-523 
A. K. Pulatov. Absence of localization of the Laplace series on the sphere for functions of the Nikol'skii class $H_1^1(S^2)$. Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 517-523. http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a6/
@article{MZM_1977_22_4_a6,
     author = {A. K. Pulatov},
     title = {Absence of localization of the {Laplace} series on the sphere for functions of the {Nikol'skii} class $H_1^1(S^2)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {517--523},
     year = {1977},
     volume = {22},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a6/}
}
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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]).