This article is cited in 1 paper

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

A. K. Pulatov

M. V. Lomonosov Moscow State University

Abstract: 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]).

UDC: 517.4

Received: 04.05.1976

 English version: Mathematical Notes, 1977, 22:4, 779–783

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