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    Wigner-von Neumann type perturbations of periodic Schrödinger operators

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    Author
    Lukic, Milivoje; Ong, Darren C.
    Date
    2015
    Abstract
    Schrödinger 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.
    Citation
    Lukic, Milivoje and Ong, Darren C.. "Wigner-von Neumann type perturbations of periodic Schrödinger operators." Transactions of the American Mathematical Society, 367, (2015) American Mathematical Society: 707-724. https://doi.org/10.1090/S0002-9947-2014-06365-4 .
    Published Version
    https://doi.org/10.1090/S0002-9947-2014-06365-4 
    Type
    Journal article
    Publisher
    American Mathematical Society
    Citable link to this page
    https://hdl.handle.net/1911/94850
    Rights
    Article 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.
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    • Faculty Publications [4918]
    • Mathematics Faculty Publications [51]

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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map