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Creators/Authors contains: "Wang, Xingya"

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  1. ; ; (, Journal of Spectral Theory)
    We study half-line Schrödinger operators with locally H^{-1} potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last-Simon-type description of the absolutely continuous spectrum and sufficient conditions for different spectral types. In the second part, we focus on potentials which are decaying in a local H^{-1} sense; we establish a spectral transition between short-range and long-range potentials and an ell^2 spectral transition for sparse singular potentials. The regularization procedure used to handle distributional potentials is also well suited for controlling rapid oscillations in the potential; thus, even within the class of smooth potentials, our results apply in situations which would not classically be considered decaying or even bounded. 
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