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 Mat. Zametki: Year: Volume: Issue: Page: Find

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

$L_p$-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 $2/(2-\alpha)<p<2/\alpha$.

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

Bibliographic databases:

UDC: 517.5

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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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
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