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MR1621882 (99g:34166) 34L40 (42B20 81Q10 81Q15)
Christ, Michael; Kiselev, Alexander Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: some optimal results. J. Amer. Math. Soc. 11 (1998), no. 4, 771–797.
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