Generalized Prüfer variables for perturbations of Jacobi and CMV matrices

Prüfer variables are a standard tool in spectral theory, developed originally for perturbations of the free Schrödinger operator. We adapt the generalized Prüfer variables, introduced by Kiselev–Remling–Simon for perturbations of an arbitrary Schrödinger operator, to the setting of Jacobi and Szegő recursions. We present an application to random L2L2 perturbations of Jacobi and CMV matrices, and an application to decaying oscillatory perturbations of periodic Jacobi and CMV matrices.