This article is cited in 2 papers

Mathematics

Spectrum of a Jacobi matrix with exponentially growing matrix elements

I. A. Sheipak

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Key words: Jacobi matrix, self-adjoint extensions of symmetric operators, asymptotics of eigenvalues, self-similar weighted function.

UDC: 511.984

Received: 01.12.2010

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