On the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbations

Abstract

We show that spectral Hausdorff dimensional properties of discrete Schrödinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component.