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

  • Authors:

  • Serguei Naboko;Irina Pchelintseva;Luis O. Silva

  • Affiliations:

  • Department of Higher Mathematics and Mathematical Physics, Institute of Physics, St. Petersburg State University, Ulyanovskaya 1. 198904, St. Petersburg, Russia;Department of Higher Mathematics and Mathematical Physics, Institute of Physics, St. Petersburg State University, Ulyanovskaya 1. 198904, St. Petersburg, Russia;Departamento de Métodos Matemáticos y Numéricos, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04 ...

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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.