I've been reading Gerald Teschl's book on Jacobi operators (and nonlinear lattices) where chapter seven shows how to compute the spectrum of a bi-infinite periodic Jacobi operator. I was wondering what can be said for the half line example, i.e. a one-way infinite periodic Jacobi operator. For instance, is the spectrum still purely absolutely continuous?

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    $\begingroup$ No, you can have eigenvalues in the gaps, and of course the multiplicity of the ac spectrum will be $1$ now. Nothing else changes. $\endgroup$ – Christian Remling Feb 1 at 20:32
  • $\begingroup$ Thanks very much! $\endgroup$ – Mathmo Feb 1 at 21:45

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