Geodesic
Indefinite Sturm--Liouville Problem for Some Classes of Self-similar Singular Weights
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 88-98

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We continue studying the asymptotics of the spectrum for the boundary value problem $-y''-\lambda \rho y=0$, $y(0)=y(1)=0$, where $\rho $ is a function in the space $\mathring W_{\!2}^{-1}[0,1]$ with a self-similar primitive. The cases of nonarithmetic and degenerate arithmetic self-similarity of such a primitive are considered. 
@article{TM_2006_255_a6,
     author = {A. A. Vladimirov and I. A. Sheipak},
     title = {Indefinite {Sturm--Liouville} {Problem} for {Some} {Classes} of {Self-similar} {Singular} {Weights}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {88--98},
     publisher = {mathdoc},
     volume = {255},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_255_a6/}
}
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A. A. Vladimirov; I. A. Sheipak. Indefinite Sturm--Liouville Problem for Some Classes of Self-similar Singular Weights. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 88-98. http://geodesic.mathdoc.fr/item/TM_2006_255_a6/