Geodesic
Equiconvergence of eigenfunction expansions for Sturm-Liouville operators with a distributional potential
Sbornik. Mathematics, Tome 201 (2010) no. 9, pp. 1307-1322

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The Sturm-Liouville operator $L=-d^2/dx^2+q(x)$ in the space $L_2[0,\pi]$ under Dirichlet boundary conditions is investigated. It is assumed that $q(x)=u'(x)$, $u(x)\in L_2[0,\pi]$ (here, differentiation is used in the distributional sense). The problem of when the expansion of a function $f(x)$ in terms of a series of eigenfunctions and associated functions of the operator $L$ is uniformly equiconvergent on the whole of the interval $[0,\pi]$ with its Fourier sine series expansion is considered. It is shown that such uniform convergence holds for any function $f(x)$ in the space $L_2[0,\pi]$. Bibliography: 22 titles.
Keywords: Sturm-Liouville operator, singular potential
Mots-clés : uniform equiconvergence. 
@article{SM_2010_201_9_a2,
     author = {I. V. Sadovnichaya},
     title = {Equiconvergence of eigenfunction expansions for {Sturm-Liouville} operators with a distributional potential},
     journal = {Sbornik. Mathematics},
     pages = {1307--1322},
     publisher = {mathdoc},
     volume = {201},
     number = {9},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_9_a2/}
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I. V. Sadovnichaya. Equiconvergence of eigenfunction expansions for Sturm-Liouville operators with a distributional potential. Sbornik. Mathematics, Tome 201 (2010) no. 9, pp. 1307-1322. http://geodesic.mathdoc.fr/item/SM_2010_201_9_a2/