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).
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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. 1–45DOI 10.4171/JST/36