12 research outputs found
A class of Schrodinger operators with decaying oscillatory potentials
We discuss Schr\"odinger operators on a half-line with decaying oscillatory
potentials, such as products of an almost periodic function and a decaying
function. We provide sufficient conditions for preservation of absolutely
continuous spectrum and give bounds on the Hausdorff dimension of the singular
part of the spectral measure. We also discuss the analogs for orthogonal
polynomials on the real line and unit circle.Comment: 18 page