A. Kiselev, Y. Last and B. Simon
Stability of Singular Spectral Types under Decaying Perturbations
(61K, AMS-LaTeX )

ABSTRACT.  We look at invariance of a.e.~boundary condition spectral behavior 
under perturbations, $W$, of half-line, continuum or discrete 
Schr\"odinger operators. We extend the results of del Rio, Simon, 
Stolz from compactly supported $W$'s to suitable short-range $W$. 
We also discuss invariance of the local Hausdorff dimension 
of spectral measures under such perturbations.