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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 4, Pages 874–899 (Mi izv2062)  

This article is cited in 4 scientific papers (total in 4 papers)

Approximation of functions by algebraic polynomials in the $L_p$ metric

V. P. Motornyi


Abstract: We introduce a new method of approximation of nonperiodic functions by algebraic polynomials. In particular, by this method we establish necessary and sufficient conditions for a function on the interval $[-1,1]$ to satisfy Hölder's condition in the $L_p$ metric.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:4, 889–914

Bibliographic databases:

UDC: 517.51
MSC: Primary 41A10; Secondary 41A25
Received: 30.07.1970

Citation: V. P. Motornyi, “Approximation of functions by algebraic polynomials in the $L_p$ metric”, Izv. Akad. Nauk SSSR Ser. Mat., 35:4 (1971), 874–899; Math. USSR-Izv., 5:4 (1971), 889–914

Citation in format AMSBIB
\Bibitem{Mot71}
\by V.~P.~Motornyi
\paper Approximation of functions by algebraic polynomials in the $L_p$ metric
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 4
\pages 874--899
\mathnet{http://mi.mathnet.ru/izv2062}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=288467}
\zmath{https://zbmath.org/?q=an:0224.41002}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 4
\pages 889--914
\crossref{https://doi.org/10.1070/IM1971v005n04ABEH001122}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Motornyi, “On the mean convergence of Fourier series in Legendre polynomials”, Math. USSR-Izv., 7:1 (1973), 131–144  mathnet  crossref  mathscinet  zmath
    2. V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117  mathnet  crossref  mathscinet  zmath
    3. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. P. Motornyi, “On the Nikol'skii and Potapov classes of functions”, Proc. Steklov Inst. Math., 293 (2016), 216–227  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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