Asymptotics of the Fourier transform of the spectral measure for Schr$ouml$dinger operators with bounded and unbounded sparse potentials

Abstract

We study the pointwise behaviour of the Fourier transform of the spectral measure for discrete one-dimensional Schrodinger operators with unbounded sparse potentials, particularly with the potentials of the special type, which give rise to the spectra with Hausdorff dimensionality between 1/2 and 1. Operators with bounded sparse potentials are also considered.