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Matematicheskie Zametki, 1968, Volume 3, Issue 6, Pages 683–691 (Mi mzm6729)  

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

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

V. L. Generozov

M. V. Lomonosov Moscow State University
Full-text PDF (529 kB) Citations (2)
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 $2/(2-\alpha)<p<2/\alpha$.
Received: 01.08.1967
English version:
Mathematical Notes, 1968, Volume 3, Issue 6, Pages 436–441
DOI: https://doi.org/10.1007/BF01110602
Bibliographic databases:
UDC: 517.5
Language: Russian
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/mzm6729}
\mathscinet{http://mathscinet.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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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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