 97201 Alexander Kiselev
 Absolutely continuous spectrum of perturbed Stark operators
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Apr 9, 97

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Abstract. We prove new results on the stability of the absolutely
continuous spectrum for onedimensional perturbed Stark operators with
decaying or
satisfying certain smoothness assumption perturbation.
We show that
the absolutely continuous spectrum of the Stark operator is
stable if the perturbing potential decays at the rate
$(1+x)^{\frac{1}{3}\epsilon}$ or if it is continuously
differentiable with derivative from the H\"older space
$C_{\alpha}(R),$ with any $\alpha>0.$
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