Sergey Simonov
An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weights
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ABSTRACT.  We consider self-adjoint unbounded Jacobi matrices with weights modulated by a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum of the matrix is either purely absolutely continuous or discrete. This constitutes an example of the spectral phase transition of the first order. We study the lines where the spectral phase transition occurs and find asymptotics of generalized eigenvectors via the Birkhoff-Adams Theorem.