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    Fourier Analysis on SU(2)

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    Author
    Leaser, Tyler
    Abstract
    The set SU(2) of 2x2 unitary matrices with determinant one forms a compact non-abelian Lie group diffeomorphic to the three dimensional sphere. This thesis surveys general theory concerning analysis on compact Lie groups and applies this in the setting of SU(2). Our principal reference is J. Faraut's book {\em Analysis on Lie Groups}. Fundamental results in representation theory with compact Lie groups include the Peter-Weyl Theorem, Plancherel Theorem and a criterion for uniform convergence of Fourier series.  On SU(2) we give explicit constructions for Haar measure and all irreducible unitary representations. For purposes of motivation and comparison we also consider analysis on U(1), the unit circle in the complex plane. In this context, the general theory specializes to yield classical results on Fourier series with periodic functions and the heat equation in one dimension. We discuss convergence behavior of Fourier series on SU(2) and show that Cauchy problem for the heat equation with continuous boundary data admits a unique solution.  
    URI
    http://hdl.handle.net/10342/4074
    Subject
     Mathematics; Analysis on SU(2); Heat equation; Lie algebra 
    Date
    2012
    Citation:
    APA:
    Leaser, Tyler. (January 2012). Fourier Analysis on SU(2) (Master's Thesis, East Carolina University). Retrieved from the Scholarship. (http://hdl.handle.net/10342/4074.)

    Display/Hide MLA, Chicago and APA citation formats.

    MLA:
    Leaser, Tyler. Fourier Analysis on SU(2). Master's Thesis. East Carolina University, January 2012. The Scholarship. http://hdl.handle.net/10342/4074. March 08, 2021.
    Chicago:
    Leaser, Tyler, “Fourier Analysis on SU(2)” (Master's Thesis., East Carolina University, January 2012).
    AMA:
    Leaser, Tyler. Fourier Analysis on SU(2) [Master's Thesis]. Greenville, NC: East Carolina University; January 2012.
    Collections
    • Master's Theses
    • Mathematics
    Publisher
    East Carolina University

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