Conference proceeding
Integral Operator Approach for Computing Certain Generalized Fourier Transforms
WMSCI 2010: 14TH WORLD MULTI-CONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL II
01 Jan 2010
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
Non-commutative harmonic analysis on locally compact groups is generally a difficult task due to the nature of the group representations. Applications of the Fourier transform of groups other than Rn have been limited due to the difficulties in numerically computing the analytical form. We present an integral operator approach with induced representations to determine the generalized Fourier transform of three dimensional semi-direct product groups. We analytically compute the Fourier transform and the inversion formula for certain semi-direct product groups given by linear transformations on the plane, specifically the Euclidean motion group; the hyber-bolic group and the Heisenberg group. This simplified approach allows numerical computation of a general Fourier transform and its inverse using non-uniform FFT methods.
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Details
- Title
- Integral Operator Approach for Computing Certain Generalized Fourier Transforms
- Creators
- Amal Aafif - Florida A&M Univ, Dept Math, 1617 S Martin Luther King Blvd, Tallahassee, FL 32310 USARobert P. Boyer - Florida A&M Univ, Dept Math, 1617 S Martin Luther King Blvd, Tallahassee, FL 32310 USA
- Contributors
- J Baralt (Editor)N Callaos (Editor)S Hashimoto (Editor)W Lesso (Editor)C D Zinn (Editor)
- Publication Details
- WMSCI 2010: 14TH WORLD MULTI-CONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL II
- Conference
- WMSCI 2010: 14TH WORLD MULTI-CONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL II, 14th
- Publisher
- Int Inst Informatics & Systemics
- Number of pages
- 5
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- [Retired Faculty]
- Identifiers
- 991019173645404721
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- Computer Science, Cybernetics
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