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    • University of Missouri-Columbia
    • Graduate School - MU Theses and Dissertations (MU)
    • Theses and Dissertations (MU)
    • Dissertations (MU)
    • 2006 Dissertations (MU)
    • 2006 MU dissertations - Freely available online
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    Topics in spectral and inverse spectral theory

    Zinchenko, Maksym, 1980-
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    Date
    2006
    Format
    Thesis
    Metadata
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    Abstract
    This dissertation is concerned with two major classes of operators and provides various spectral and inverse spectral results for them. In the first part of this work a special class of one-dimensional discrete unitary operators is under investigation. The underlying Weyl-Titchmarsh theory and a Borg-type inverse spectral result are established for this class of operators. The second part of this work is devoted to some spectral theoretical questions for one- and multi-dimensional Schrödinger operators. In particular, the Weyl-Titchmarsh theory for one-dimensional self-adjoint Schrödinger operators with strongly singular potentials is established. In addition, a general perturbation theory for non-self-adjoint operators is developed and subsequently applied to a large class of non-self-adjoint multi-dimensional Schrödinger operators.
    URI
    https://hdl.handle.net/10355/4460
    https://doi.org/10.32469/10355/4460
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
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    • 2006 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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