Geodesic
Spectrum of a Jacobi matrix with exponentially growing matrix elements
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 15-21

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A Jacobi matrix with an exponential growth of its elements and the corresponding symmetric operator are considered. It is proved that the eigenvalue problem for some self-adjoint extension of the operator in some Hilbert space is equivalent to the eigenvalue problem of the Sturm–Liouville operator with a discrete self-similar weight. An asymptotic formula for the distribution of eigenvalues is obtained. 
@article{VMUMM_2011_6_a3,
     author = {I. A. Sheipak},
     title = {Spectrum of a {Jacobi} matrix with exponentially growing matrix elements},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {15--21},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_6_a3/}
}
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I. A. Sheipak. Spectrum of a Jacobi matrix with exponentially growing matrix elements. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 15-21. http://geodesic.mathdoc.fr/item/VMUMM_2011_6_a3/