Lukic, MilivojeOng, Darren C.2017-06-142017-06-142015Lukic, Milivoje and Ong, Darren C.. "Wigner-von Neumann type perturbations of periodic Schrödinger operators." <i>Transactions of the American Mathematical Society,</i> 367, (2015) American Mathematical Society: 707-724. https://doi.org/10.1090/S0002-9947-2014-06365-4 .https://hdl.handle.net/1911/94850Schrödinger operators on the half line. More precisely, the perturbations we consider satisfy a generalized bounded variation condition at infinity and an LP decay condition. We show that the absolutely continuous spectrum is preserved, and give bounds on the Hausdorff dimension of the singular part of the resulting perturbed measure. Under additional assumptions, we instead show that the singular part embedded in the essential spectrum is contained in an explicit countable set. Finally, we demonstrate that this explicit countable set is optimal. That is, for every point in this set there is an open and dense class of periodic Schrödinger operators for which an appropriate perturbation will result in the spectrum having an embedded eigenvalue at that point.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlehttps://doi.org/10.1090/S0002-9947-2014-06365-4