On the spectrum of periodic perturbations of certain unbounded Jacobi operators

It is known that a purely off-diagonal Jacobi operator with coefficients \(a_n=n^{\alpha}\), \(\alpha\in(0,1]\), has a purely absolutely continuous spectrum filling the whole real axis. We show that a 2-periodic perturbation of these operators creates a non trivial gap in the spectrum.

Abstract licence: CC BY

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