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On the spectrum of periodic perturbations of certain unbounded Jacobi operators

Sahbani J.

Opuscula Mathematica

2016

Vol. 36, no. 6

807--818

It is known that a purely off-diagonal Jacobi operator with coefficients [formula] 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.