The absence of singular continuous spectrum for perturbed Jacobi operators

This paper is mainly about the spectral properties of a class of Jacobi operators \(({H_{c,b}}u)(n) = {c_n}u(n + 1) + {c_{n - 1}}u(n - 1) + {b_n}u(n),\) $$(H_{c,b}u)(n)=c_{n}u(n+1)+c_{n-1}u(n-1)+b_{n}u(n),$$ 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.