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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 2, Pages 369–392 (Mi izv1359)  

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


Abstract: This paper establishes best possible conditions, on the degree of approximation of functions $f(x_1,…,x_m)$ 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.

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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:2, 347–369

Bibliographic databases:

UDC: 517.5
MSC: 41A20, 26B05
Received: 27.05.1983

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”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 369–392; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 2
\pages 369--392
\mathnet{http://mi.mathnet.ru/izv1359}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=791308}
\zmath{https://zbmath.org/?q=an:0605.41015}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 347--369
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001151}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Komarov M.A., “Distribution of the Logarithmic Derivative of a Rational Function on the Line”, Acta Math. Hung.  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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