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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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