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On optimal separation of eigenvalues for a quasiperiodic Jacobi matrix. (English) Zbl 1312.47036
The authors consider a quasiperiodic Jacobi operator \(H(x,w)\) with analytic coefficients defined on \(l^2(\mathbb{Z})\), in the regime of the positive Lyapunov exponent of the cocycle associated with \(H(x,w)\).
The main result states that any eigenvalue of the finite Jacobi submatrix \(H^{(N)}(z,w)\) of \(H(x,w)\) on \([0,N-1] \) is separated from the rest of the spectrum by \(\displaystyle \frac{1}{N(\log N)^p}\), with \(p>15\). This result improves the known separation result for Schrödinger quasiperiodic operators.

MSC:
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
47A10 Spectrum, resolvent
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
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