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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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}