 962 Kiselev A.
 Absolutely Continuous Spectrum of OneDimensional
Schr\"odinger Operators and Jacobi Matrices with
Slowly Decreasing Potentials
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Jan 3, 96

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Abstract. We prove that for any onedimensional 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 semiaxis. 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.
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962.tex