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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.

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)
Full Text: DOI arXiv
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