Abstract
Consider an arbitrary periodic Jacobi matrix J per ,with periodic weights c n . A class of unbounded Jacobi matrices A + cB is investigated, where B is a diagonal matrix and A is a Jacobi matrix with zero main diagonal and modulated weights λ n (e.g. λ n = c n n α , α > 0). Depending on whether the coupling constant (-c) belongs to the absolutely continuous spectrum of J per or not, the spectrum of A + cB is either pure absolutely continuous or discrete. This gives us a class of examples with multithreshold spectral phase transition phenomena.
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