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MR1639550 (99h:34124) 34L40 (42B25 47E05 47G10 81Q10)
Kiselev, Alexander Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and a.e. convergence of integral operators. Duke Math. J. 94 (1998), no. 3, 619--646.
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