Spectrum of a Jacobi Matrix with Exponentially Growing Matrix Elements / Sheipak I.A. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 6. P. 15-21 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
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 this 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.
Jacobi matrix, self-adjoint extensions of symmetric operators,
asymptotics of eigenvalues, self-similar weighted function.