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Non-commutative harmonic analysis on certain semi-direct product groups
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http://hdl.handle.net/1860/1767
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| 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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