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    The Spectral Theorem for Self-Adjoint Operators

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    Author
    Chilcoat, Kenneth
    Abstract
    The Spectral Theorem for Self-Adjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing a functional calculus that extends the intuitive notion of evaluating a polynomial on an operator. The Spectral Theorem is fundamentally important to operator theory and has applications in many fields, especially harmonic analysis on locally compact abelian groups. This thesis represents a merging of two traditional treatments of the Spectral Theorem and includes an extended example highlighting an important application in harmonic analysis.
    URI
    http://hdl.handle.net/10342/5344
    Subject
    Hilbert Space
    Date
    2016-04-25
    Citation:
    APA:
    Chilcoat, Kenneth. (April 2016). The Spectral Theorem for Self-Adjoint Operators (Master's Thesis, East Carolina University). Retrieved from the Scholarship. (http://hdl.handle.net/10342/5344.)

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    MLA:
    Chilcoat, Kenneth. The Spectral Theorem for Self-Adjoint Operators. Master's Thesis. East Carolina University, April 2016. The Scholarship. http://hdl.handle.net/10342/5344. August 11, 2022.
    Chicago:
    Chilcoat, Kenneth, “The Spectral Theorem for Self-Adjoint Operators” (Master's Thesis., East Carolina University, April 2016).
    AMA:
    Chilcoat, Kenneth. The Spectral Theorem for Self-Adjoint Operators [Master's Thesis]. Greenville, NC: East Carolina University; April 2016.
    Collections
    • Master's Theses
    • Mathematics
    Publisher
    East Carolina University

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