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Please use this identifier to cite or link to this item: http://hdl.handle.net/1860/1767

Title: Non-commutative harmonic analysis on certain semi-direct product groups
Authors: Aafif, Amal
Keywords: Mathematics;Group theory;Harmonic analysis
Issue Date: 4-Sep-2007
Abstract: Non-commutative harmonic analysis on locally compact groups is generally a difficult task due to the nature of the group representations. We present an integral operator approach with induced representations to compute the generalized Fourier transform of three dimensional semi-direct product groups. We begin with an overview of representation theory and harmonic analysis on locally compact abelian groups, compact groups and locally compact separable Type I groups. We describe induced representations and the corresponding character formulas. We analytically compute the Fourier transform and the inversion formula for semi-direct product groups given by linear transformations on the plane. Finally, numerical results are presented for the Euclidean motion group and the hyperbolic motion group.
URI: http://hdl.handle.net/1860/1767
Appears in Collections:Drexel Theses and Dissertations

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