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Self-similar functions in $L_2[0,1]$ and Sturm--Liouville Problem with singular indefinite weight

I. A. Sheipak·A. A. Vladimirov
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Abstract

In the paper the Sturm-Liouville problem $-y''-ρy=0$, $y(0)=y(1)=0$ is studied. $ρ$ is a generalized derivative of function $P\in L_2[0,1]$. For self-similar $P$ asymptotic formulas for eigenvalues are obtained.

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I. A. Sheipak, A. A. Vladimirov. 2005-07-01. Self-similar functions in $L_2[0,1]$ and Sturm--Liouville Problem with singular indefinite weight. https://arxiv.org/abs/math/0405410

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