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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157311For 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.27 pages, 2 figuresMathematical Physics47B36; 47A25; 39A11; 39A12Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysistext