Spectra of some selfadjoint Jacobi operators in the double root case

Abstract

In this paper we prove a mixed spectrum of Jacobi operators defined by $\lambda_n=s(n)(1+x(n))$ and $q_n=-2s(n)(1+y(n))$, where $(s(n))$ is a real unbounded sequence, $(x(n))$ and $(y(n))$ are some perturbations.