Geodesic
$L_p$-convergence for expansions in terms of the eigenfunctions of a~Sturm-Liouville problem
Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 683-691

Voir la notice de l'article provenant de la source Math-Net.Ru

For the operator $Ly=-(x^{2\alpha}y')'$, $x\in[0,1]$, $y(0)=y(1)=0$ with $0\leqslant\alpha1/2$, or $|y|\infty$, $y(1)=0$ with $1/2\leqslant\alpha1$ 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 $2/(2-\alpha)$. 
@article{MZM_1968_3_6_a7,
     author = {V. L. Generozov},
     title = {$L_p$-convergence for expansions in terms of the eigenfunctions of {a~Sturm-Liouville} problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {683--691},
     publisher = {mathdoc},
     volume = {3},
     number = {6},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a7/}
}
TY  - JOUR
AU  - V. L. Generozov
TI  - $L_p$-convergence for expansions in terms of the eigenfunctions of a~Sturm-Liouville problem
JO  - Matematičeskie zametki
PY  - 1968
SP  - 683
EP  - 691
VL  - 3
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a7/
LA  - ru
ID  - MZM_1968_3_6_a7
ER  - 
%0 Journal Article
%A V. L. Generozov
%T $L_p$-convergence for expansions in terms of the eigenfunctions of a~Sturm-Liouville problem
%J Matematičeskie zametki
%D 1968
%P 683-691
%V 3
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a7/
%G ru
%F MZM_1968_3_6_a7
V. L. Generozov. $L_p$-convergence for expansions in terms of the eigenfunctions of a~Sturm-Liouville problem. Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 683-691. http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a7/