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 Mat. Zametki, 1977, Volume 22, Issue 4, Pages 517–523 (Mi mz8073)

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]).

Full text: PDF file (403 kB)

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

Bibliographic databases:

UDC: 517.4

Citation: A. K. Pulatov, “Absence of localization of the Laplace series on the sphere for functions of the Nikol'skii class $H_1^1(S^2)$”, Mat. Zametki, 22:4 (1977), 517–523; Math. Notes, 22:4 (1977), 779–783

Citation in format AMSBIB
\Bibitem{Pul77}
\by A.~K.~Pulatov
\paper Absence of localization of the Laplace series on the sphere for functions of the Nikol'skii class $H_1^1(S^2)$
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 4
\pages 517--523
\mathnet{http://mi.mathnet.ru/mz8073}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=499935}
\zmath{https://zbmath.org/?q=an:0363.42008}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 4
\pages 779--783
\crossref{https://doi.org/10.1007/BF01146423}