On spectral asymptotics of the Neumann problem for the Sturm-Liouville equation with arithmetically self-similar weight of a generalized Cantor type. (English. Russian original) Zbl 1394.34183
Funct. Anal. Appl. 52, No. 1, 70-73 (2018); translation from Funkts. Anal. Prilozh. 52, No. 1, 85-88 (2018).
From the summary and introduction: This work introduces a new method for estimating the eigenvalue counting function. This makes it possible to consider a much wider class of self-similar measures.
In this paper we study the spectral asymptotics of the problem \[ \begin{gathered} -y''=\lambda\rho y,\\ y'(0)= y'(1)= 0,\end{gathered} \] where the weight measure \(\rho\) is a distributional derivative of a self-similar generalized Cantor-type function (in particular, \(\rho\) is singular with respect to the Lebesgue measure).
In this paper we study the spectral asymptotics of the problem \[ \begin{gathered} -y''=\lambda\rho y,\\ y'(0)= y'(1)= 0,\end{gathered} \] where the weight measure \(\rho\) is a distributional derivative of a self-similar generalized Cantor-type function (in particular, \(\rho\) is singular with respect to the Lebesgue measure).
MSC:
| 34L20 | Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators |
| 34B24 | Sturm-Liouville theory |
References:
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