  We study localization effects of disorder on the spectral and dynamical
properties of Schroedinger operators with random potentials. The new results
include exponentially decaying bounds on the transition amplitude and related
projection kernels, including in the mean. These are derived through the
analysis of fractional moments of the resolvent, which are finite due to the
resonance-diffusing effects of the disorder. The main difficulty which has up
to now prevented an extension of this method to the continuum can be traced to
the lack of a uniform bound on the Lifshitz-Krein spectral shift associated
with the local potential terms. The difficulty is avoided here through the use
of a weak-L1 estimate concerning the boundary-value distribution of resolvents
of maximally dissipative operators, combined with standard tools of relative
compactness theory.
