Abstract. We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we nd new classes of perturbations, characterized mainly by smoothness conditions, which preserve purely absolutely continuous spectrum. Then we establish stability of the absolutely continuous spectrum in more general situations, where imbedded singular spectrum may occur. We present two kinds of optimal conditions for the stability of absolutely continuous spectrum: decay and smoothness. In the decay direction, we show that a sucient (in the power scale) condition is jq(x)j C(1 + jxj) 1
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