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Mathematics of the USSR-Izvestiya, 1988, Volume 30, Issue 3, Pages 599–614
DOI: https://doi.org/10.1070/IM1988v030n03ABEH001032
(Mi im1312)
 

This article is cited in 17 scientific papers (total in 18 papers)

Approximation of functions on the sphere

S. M. Nikol'skii, P. I. Lizorkin
References:
Abstract: The authors consider classes $H_p^r(\sigma)$ of functions $f$ on a sphere $\sigma$, whose smoothness is determined by the properties of differences along geodesics (duly averaged) in the metric of $L_p(\sigma)$. An integral representation of a function $f \in L_p(\sigma)$ is obtained in terms of the differences mentioned. On this basis direct and inverse theorems on approximation of functions $f \in H_p^r(\sigma)$ be polynomials in spherical harmonics are established. These theorems completely characterize the class $H_p^r(\sigma)$.
Bibliography: 9 titles.
Received: 21.03.1986
Bibliographic databases:
Document Type: Article
UDC: 517.518
MSC: Primary 41A10, 41A63, 41A25; Secondary 41A17
Language: English
Original paper language: Russian
Citation: S. M. Nikol'skii, P. I. Lizorkin, “Approximation of functions on the sphere”, Math. USSR-Izv., 30:3 (1988), 599–614
Citation in format AMSBIB
\Bibitem{NikLiz87}
\by S.~M.~Nikol'skii, P.~I.~Lizorkin
\paper Approximation of functions on the sphere
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 3
\pages 599--614
\mathnet{http://mi.mathnet.ru//eng/im1312}
\crossref{https://doi.org/10.1070/IM1988v030n03ABEH001032}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=903627}
\zmath{https://zbmath.org/?q=an:0717.41061|0665.41018}
Linking options:
  • https://www.mathnet.ru/eng/im1312
  • https://doi.org/10.1070/IM1988v030n03ABEH001032
  • https://www.mathnet.ru/eng/im/v51/i3/p635
  • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:667
    Russian version PDF:243
    English version PDF:27
    References:80
    First page:2
     
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