Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis |
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| Authors: | Serguei Naboko Irina Pchelintseva Luis O Silva |
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| Institution: | aDepartment of Higher Mathematics and Mathematical Physics, Institute of Physics, St. Petersburg State University, Ulyanovskaya 1. 198904, St. Petersburg, Russia;bDepartamento de Métodos Matemáticos y Numéricos, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510, México D.F., Mexico |
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| 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. |
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| Keywords: | Jacobi matrices Uniform asymptotics First-order spectral phase transition Discrete spectrum |
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