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    • 2017 Dissertations (MU)
    • 2017 MU dissertations - Freely available online
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    Radiation conditions and integral representations for Clifford algebra-valued null solutions of the iterated perturbed Dirac operator

    Okamoto, Nicholas H
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    Date
    2017
    Format
    Thesis
    Metadata
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    Abstract
    In 1912 Arnold Sommerfeld introduced a special decay condition at infinity to address uniqueness issues for certain boundary value problems involving the Helmholtz operator in an exterior domain. Examples of such boundary value problems arise in optical diffraction theory and radio wave propagation. This decay condition, which has become known as Sommerfeld’s radiation condition, has been subsequently adapted to various other operators of interest in mathematics, engineering, and physics. Examples include the Silver-Muller radiation condition for the Maxwell system, and radiation conditions for certain perturbed Dirac operators. In this dissertation, we continue this line of research by considering iterated perturbed Dirac operators. Among other things, suitable radiation conditions are identified which allow us to prove integral representation formulas for Clifford algebra-valued null-solutions of iterated perturbed Dirac operators.
    URI
    https://hdl.handle.net/10355/65431
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
    Collections
    • 2017 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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