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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
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\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:
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This publication is cited in the following articles:
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V. P. Motornyi, “On the mean convergence of Fourier series in Legendre polynomials”, Math. USSR-Izv., 7:1 (1973), 131–144
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V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117
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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
  -
V. P. Motornyi, “On the Nikol'skii and Potapov classes of functions”, Proc. Steklov Inst. Math., 293 (2016), 216–227
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