Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis

Serguei Naboko,Irina Pchelintseva,Luis O. Silva

Journal of Approximation Theory（2009）

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摘要

For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end, we develop a method for obtaining uniform asymptotics, with respect to the spectral parameter, of the generalized eigenvectors. Our technique can be applied to a wide range of Jacobi matrices.

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关键词

jacobi matrix,jacobi matrices,first-order spectral phase transition,discrete spectrum,positive real axis,uniform asymptotic analysis,uniform asymptotics,critical coupling case,discrete spectrum.,transition boundary,generalized eigenvectors,wide range,spectral parameter,two-parameter family,phase transition,eigenvectors,spectrum,first order,asymptotic analysis

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