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.