Kiselev A.
Absolutely Continuous Spectrum of One-Dimensional 
Schr\"odinger Operators and Jacobi Matrices with 
Slowly Decreasing Potentials
(71K, LaTeX)

ABSTRACT.  We prove that for any one-dimensional Schr\"odinger operator 
with potential $V(x)$ satisfying decay condition $|V(x)| 
\leq Cx^{-3/4-\epsilon},$ the absolutely continuous spectrum 
fills the whole positive semi-axis. The description of the set 
in $\R^{+}$ on which the singular part of the spectral measure 
might be supported is also given. Analogous results hold for 
Jacobi matrices.