An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size contained in an interval of size
Ilia Binder
University of Toronto, Toronto, Ontario, CanadaMircea Voda
The University of Chicago, USA
![An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size $n$ contained in an interval of size $n^{–C}$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-3-issue-1.png&w=3840&q=90)
Abstract
We consider infinite quasi-periodic Jacobi self-adjoint matrices for which the three main diagonals are given via values of real analytic functions on the trajectory of the shift . We assume that the Lyapunov exponent of the corresponding Jacobi cocycle satisfies . In this setting we prove that the number of eigenvalues of a submatrix of size contained in an interval centered at with does not exceed for any . Here , and , , are constants depending on (and the other parameters of the problem).
Cite this article
Ilia Binder, Mircea Voda, An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size contained in an interval of size . J. Spectr. Theory 3 (2013), no. 1, pp. 1–45
DOI 10.4171/JST/36