Geodesic
Asymptotics of the Eigenvalues of the Sturm--Liouville Problem with Discrete Self-Similar Weight
Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 662-672

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We study the asymptotics of the spectrum of the boundary-value problem $$ -y''-\lambda\rho y=0,\qquad y(0)=y(1)=0, $$ for the case in which the weight $\rho\in\mathring W_2^{-1}[0,1]$ is the generalized (in the sense of distributions) derivative of a self-similar function $P\in L_2[0,1]$ of zero spectral order.
Mots-clés : Sturm–Liouville problem, Sturm–Liouville problem.
Keywords: asymptotics of eigenvalues, self-similar function, spectral order of a function 
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     author = {A. A. Vladimirov and I. A. Sheipak},
     title = {Asymptotics of the {Eigenvalues} of the {Sturm--Liouville} {Problem} with {Discrete} {Self-Similar} {Weight}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {662--672},
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     volume = {88},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a2/}
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A. A. Vladimirov; I. A. Sheipak. Asymptotics of the Eigenvalues of the Sturm--Liouville Problem with Discrete Self-Similar Weight. Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 662-672. http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a2/