Periodic Jacobi operator with finitely supported perturbations

Abstract

We describe the spectral properties of the Jacobi operator $(Hy{)}_n=a_{n-1}{y}_{n-1}+a_n{y}_{n+1}+b_n{y}_n,$ $n\in \mathbb{Z},$ with $a_n=a_n^0+u_n,$ $b_n=b_n^0+v_n,$ where sequences $a_n^0>0,$ $b_n^0\in \mathbb{R}$ are periodic with period $q$, and sequences $u_n,$ $v_n$ have compact support. In the case $u_n\equiv 0$ we obtain the asymptotics of the spectrum in the limit of small perturbations $v_n.$

References in corpus (4)

• Scattering Theory for Jacobi Operators with Quasi-Periodic Background
• Marchenko-Ostrovski mappings for periodic Jacobi matrices
• 1D Schrödinger operator with periodic plus compactly supported potentials
• Inverse resonance scattering for Jacobi operators

Cited by in corpus (3)

• Resonances for large one-dimensional "ergodic" systems
• Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices
• Eigenvalues of periodic difference operators on lattice octant