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Dissertation
Non-commutative harmonic analysis on certain semi-direct product groups
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2007
DOI:
https://doi.org/10.17918/etd-1767
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.
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Details
- Title
- Non-commutative harmonic analysis on certain semi-direct product groups
- Creators
- Amal Aafif - DU
- Contributors
- Robert Paul Boyer (Advisor) - Drexel University (1970-)Werner Krandick (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 1767; 991014632696504721