Geodesic
Asymptotics of the Spectrum of a Differential Operator with the Weight Generated by the Minkowski Function
Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 302-308.

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This paper is devoted to the study of the asymptotics of the spectrum of the boundary-value problem $$ -y''-\lambda\rho y=0, \qquad y(0)=y(1)=0, $$ where $\rho$ is the generalized derivative of the Minkowski function, i.e., $\rho=?'(x)$ (here $?(x)$ is the “question-mark function” first defined by Minkowski, who introduced this notation). For the eigenvalues of the problem, asymptotic two-sided estimates of power type are obtained. The order of the power is determined by the Hausdorff dimension of the support of the Minkowski measure $d?$.
Keywords: spectrum of a differential operator, Minkowski function, boundary-value problem, Minkowski measure.
Mots-clés : Hausdorff dimension 
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I. A. Sheipak. Asymptotics of the Spectrum of a Differential Operator with the Weight Generated by the Minkowski Function. Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 302-308. http://geodesic.mathdoc.fr/item/MZM_2015_97_2_a12/

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