The Kunz-Souillard approach to localization for Jacobi operators

Abstract

In this paper we study spectral properties of Jacobi operators. In particular, we prove two main results: (1) that perturbing the diagonal coefficients of Jacobi operator, in an appropriate sense, results in exponential localization, and purely pure point spectrum with exponentially decaying eigenfunctions; and (2) we present examples of decaying potentials $b_n$ such that the corresponding Jacobi operators have purely pure point spectrum.