Article ID Journal Published Year Pages File Type
4607863 Journal of Approximation Theory 2009 23 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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