 96373 F. Gesztesy and B. Simon
 Inverse Spectral Analysis with Partial Information on the Potential, I.
The Case of an A.C. Component in the Spectrum
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Aug 19, 96

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Abstract. We consider operators $\frac{d^2}{dx^2} + V$ in $L^2 (\Bbb R)$ with
the sole hypothesis that $V$ is limit point at $\pm\infty$ and that
$\frac{d^2}{dx^2} + V$ in $L^2 ((0,\infty))$ has some absolutely
continuous component $S_+$ in its spectrum. We prove that $V$ on
$(\infty,0)$ is completely determined by knowledge of $V$ on
$(0,\infty)$ and by the reflection coefficient $R_+(\lambda)$ for
scattering from right incidence and energies $\lambda \in S$, where
$S \subseteq S_+$ has positive Lebesgue measure.
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