The absence of singular continuous spectrum for perturbed Jacobi operators

Abstract

This paper is mainly about the spectral properties of a class of Jacobi operators

$$({H_{c,b}}u)(n) = {c_n}u(n + 1) + {c_{n - 1}}u(n - 1) + {b_n}u(n),$$

where ∣c_n − 1∣ = O(n^−α) and b_n = O(n⁻¹). We will show that, for α ≥ 1, the singular continuous spectrum of the operator is empty.