The Kunz-Souillard approach to localization for Jacobi operators

2016/09/19 by Bucaj, Valmir
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1609.05703

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.

Related

• On the Kunz-Souillard approach to localization for the discrete one dimensional generalized Anderson model
• Spectral properties of dynamical localization for Schrödinger operators
• Localization of the 1D Non-Stationary Anderson Model
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
• Localization for random operators with non-monotone potentials with exponentially decaying correlations