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Mat. Zametki, 1968, Volume 3, Issue 6, Pages 683–691 (Mi mz6729)  

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

$L_p$-convergence for expansions in terms of the eigenfunctions of a Sturm-Liouville problem

V. L. Generozov

M. V. Lomonosov Moscow State University

Abstract: For the operator $Ly=-(x^{2\alpha}y')'$, $x\in[0,1]$, $y(0)=y(1)=0$ with $0\leqslant\alpha<1/2$, or $|y|<\infty$, $y(1)=0$ with $1/2\leqslant\alpha<1$ we investigate the effect which the singularity of the Sturm–Liouville operator derived from this self-adjoint expression has on $L_p$-convergence of expansions in terms of the eigenfunctions of this operator. We will prove that the orthonormalized system of eigenfunctions forms a basis in $L_p[0,1]$ for $2/(2-\alpha)<p<2/\alpha$.

Full text: PDF file (529 kB)

English version:
Mathematical Notes, 1968, 3:6, 436–441

Bibliographic databases:

UDC: 517.5
Received: 01.08.1967

Citation: V. L. Generozov, “$L_p$-convergence for expansions in terms of the eigenfunctions of a Sturm-Liouville problem”, Mat. Zametki, 3:6 (1968), 683–691; Math. Notes, 3:6 (1968), 436–441

Citation in format AMSBIB
\Bibitem{Gen68}
\by V.~L.~Generozov
\paper $L_p$-convergence for expansions in terms of the eigenfunctions of a~Sturm-Liouville problem
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 6
\pages 683--691
\mathnet{http://mi.mathnet.ru/mz6729}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=239170}
\zmath{https://zbmath.org/?q=an:0175.06601}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 6
\pages 436--441
\crossref{https://doi.org/10.1007/BF01110602}


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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. V. M. Badkov, “Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval”, Math. USSR-Sb., 24:2 (1974), 223–256  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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