Geodesic
Self-similar functions in $L_2[0,1]$ and the
Sbornik. Mathematics, Tome 197 (2006) no. 11, pp. 1569-1586

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The question of the asymptotic behaviour of the spectrum of the boundary value problem \begin{equation*} -y''-\lambda\rho y=0, \qquad y(0)=y(1)=0, \end{equation*} is considered, where $\rho$ is a function in $\mathring W_2^{-1}[0,1]$ with arithmetically self-similar primitive function. It is not assumed here that the weight $\rho$ has a constant sign. The theoretical results obtained are illustrated by the data of numerical calculations. Bibliography: 10 titles. 
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     author = {A. A. Vladimirov and I. A. Sheipak},
     title = {Self-similar functions in $L_2[0,1]$ and the},
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     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_11_a1/}
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A. A. Vladimirov; I. A. Sheipak. Self-similar functions in $L_2[0,1]$ and the. Sbornik. Mathematics, Tome 197 (2006) no. 11, pp. 1569-1586. http://geodesic.mathdoc.fr/item/SM_2006_197_11_a1/