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Mathematics of the USSR-Izvestiya, 1986, Volume 26, Issue 2, Pages 347–369
DOI: https://doi.org/10.1070/IM1986v026n02ABEH001151
(Mi im1359)
 

This article is cited in 1 scientific paper (total in 1 paper)

On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions

E. A. Sevast'yanov
References:
Abstract: This paper establishes best possible conditions, on the degree of approximation of functions $f(x_1,\dots,x_m)$ in $L_p([0,1]^m)$ ($0<p\leqslant\infty$) by rational functions, that guarantee that the function $f$ has a $p$th mean differential of order $\lambda>0$ everywhere except on a set of zero Hausdorff ($m-1+\alpha$) measure ($0<\alpha\leqslant1$).
Bibliography: 11 titles.
Received: 27.05.1983
Bibliographic databases:
UDC: 517.5
MSC: 41A20, 26B05
Language: English
Original paper language: Russian
Citation: E. A. Sevast'yanov, “On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions”, Math. USSR-Izv., 26:2 (1986), 347–369
Citation in format AMSBIB
\Bibitem{Sev85}
\by E.~A.~Sevast'yanov
\paper On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 347--369
\mathnet{http://mi.mathnet.ru//eng/im1359}
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001151}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=791308}
\zmath{https://zbmath.org/?q=an:0605.41015}
Linking options:
  • https://www.mathnet.ru/eng/im1359
  • https://doi.org/10.1070/IM1986v026n02ABEH001151
  • https://www.mathnet.ru/eng/im/v49/i2/p369
  • This publication is cited in the following 1 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:311
    Russian version PDF:99
    English version PDF:22
    References:89
    First page:1
     
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