Sparse potentials with fractional Hausdorff dimension

摘要

We construct non-random bounded discrete half-line Schrodinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case we prove and compute an exact dimension of the spectral measures. (C) 2003 Elsevier Inc. All rights reserved. [References: 10]