Fourier Analysis on SU(2)

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dc.contributor.advisorBenson, Chalen_US
dc.contributor.authorLeaser, Tyleren_US
dc.contributor.departmentMathematicsen_US
dc.date.accessioned2013-01-15T12:40:58Z
dc.date.available2013-01-15T12:40:58Z
dc.date.issued2012en_US
dc.description.abstractThe 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.  en_US
dc.description.degreeM.A.en_US
dc.format.extent125 p.en_US
dc.format.mediumdissertations, academicen_US
dc.identifier.urihttp://hdl.handle.net/10342/4074
dc.language.isoen_US
dc.publisherEast Carolina Universityen_US
dc.subjectMathematicsen_US
dc.subjectAnalysis on SU(2)en_US
dc.subjectHeat equationen_US
dc.subjectLie algebraen_US
dc.subject.lcshFourier analysis
dc.subject.lcshLie groups
dc.titleFourier Analysis on SU(2)en_US
dc.typeMaster's Thesisen_US

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