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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 1, Pages 135–147 (Mi izv2217)  

This article is cited in 2 scientific papers (total in 2 papers)

On the mean convergence of Fourier series in Legendre polynomials

V. P. Motornyi


Abstract: In this paper we study the convergence of Fourier series in Legendre polynomials in the space $L_p$, if $1\leqslant p\leqslant4/3$ or $4\leqslant p<\infty$ (i.e. in the case when the Lebesgue constants are unbounded). The fundamental result consists in the fact that with the improvement of the differential-difference properties of the function, the convergence is less affected by the growth of the Lebesgue constant ($1\leqslant p\leqslant4/3$). For functions with sufficiently good differential-difference properties the partial sums of the Fourier–Legendre series give an approximation in the $L_p$ ($1<p\leqslant4/3$) metric of an order as good as the best.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:1, 131–144

Bibliographic databases:

UDC: 517.512.6
MSC: Primary 42A20, 42A56; Secondary 41A50
Received: 10.07.1971

Citation: V. P. Motornyi, “On the mean convergence of Fourier series in Legendre polynomials”, Izv. Akad. Nauk SSSR Ser. Mat., 37:1 (1973), 135–147; Math. USSR-Izv., 7:1 (1973), 131–144

Citation in format AMSBIB
\Bibitem{Mot73}
\by V.~P.~Motornyi
\paper On the mean convergence of Fourier series in Legendre polynomials
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 1
\pages 135--147
\mathnet{http://mi.mathnet.ru/izv2217}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=340940}
\zmath{https://zbmath.org/?q=an:0258.42019}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 1
\pages 131--144
\crossref{https://doi.org/10.1070/IM1973v007n01ABEH001929}


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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. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117  mathnet  crossref  mathscinet  zmath
    2. S. B. Vakarchuk, “O priblizhenii klassicheskimi ortogonalnymi polinomami s vesom v prostranstvakh $L_{2,\gamma}(a,b)$ i o poperechnikakh funktsionalnykh klassov”, Izv. vuzov. Matem., 2019, no. 12, 37–51  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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