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Unique characterization of the Fourier transform in the framework of representation theory

Hendrik De Bie UGent, Roy Oste UGent and Joris Van der Jeugt UGent (2015) Journal of Physics : Conference Series. In Journal of Physics Conference Series 597.
abstract
In this paper we elaborate upon the investigation initiated in [3] of typical and distinctive properties of the Fourier transform (FT), in particular the crucial role played by the Howe dual pair (O(m), sl(2)). We prove in detail a result on the unique characterization of the FT making extensive use of a representation of the Lie algebra sl(2). As an example, we consider the case m = 1. We refer to [3] for a detailed study involving the derivation of a class of operators portraying FT symmetry properties.
Please use this url to cite or link to this publication:
author
organization
year
type
conference (proceedingsPaper)
publication status
published
subject
keyword
Generalized Fourier Transform
in
Journal of Physics : Conference Series
editor
Fred Brackx UGent, Hennie De Schepper UGent and Joris Van der Jeugt UGent
series title
Journal of Physics Conference Series
volume
597
issue title
XXXth International colloquium on group theoretical methods in physics (ICGTMP)
article number
012026
pages
9 pages
publisher
IOP
place of publication
Bristol, UK
conference name
30th International colloquium on Group Theoretical Methods in Physics (ICGTMP)
conference location
Ghent, Belgium
conference start
2014-07-14
conference end
2014-07-18
Web of Science type
Proceedings Paper
Web of Science id
000354929400026
ISSN
1742-6588
DOI
10.1088/1742-6596/597/1/012026
language
English
UGent publication?
yes
classification
P1
copyright statement
I have retained and own the full copyright for this publication
id
5991434
handle
http://hdl.handle.net/1854/LU-5991434
date created
2015-06-12 08:57:08
date last changed
2017-01-02 09:53:23
@inproceedings{5991434,
  abstract     = {In this paper we elaborate upon the investigation initiated in [3] of typical and distinctive properties of the Fourier transform (FT), in particular the crucial role played by the Howe dual pair (O(m), sl(2)). We prove in detail a result on the unique characterization of the FT making extensive use of a representation of the Lie algebra sl(2). As an example, we consider the case m = 1. We refer to [3] for a detailed study involving the derivation of a class of operators portraying FT symmetry properties.},
  articleno    = {012026},
  author       = {De Bie, Hendrik and Oste, Roy and Van der Jeugt, Joris},
  booktitle    = {Journal of Physics : Conference Series},
  editor       = {Brackx, Fred and De Schepper, Hennie and Van der Jeugt, Joris},
  issn         = {1742-6588},
  keyword      = {Generalized Fourier Transform},
  language     = {eng},
  location     = {Ghent, Belgium},
  pages        = {9},
  publisher    = {IOP},
  title        = {Unique characterization of the Fourier transform in the framework of representation theory},
  url          = {http://dx.doi.org/10.1088/1742-6596/597/1/012026},
  volume       = {597},
  year         = {2015},
}

Chicago
De Bie, Hendrik, Roy Oste, and Joris Van der Jeugt. 2015. “Unique Characterization of the Fourier Transform in the Framework of Representation Theory.” In Journal of Physics : Conference Series, ed. Fred Brackx, Hennie De Schepper, and Joris Van der Jeugt. Vol. 597. Bristol, UK: IOP.
APA
De Bie, H., Oste, R., & Van der Jeugt, J. (2015). Unique characterization of the Fourier transform in the framework of representation theory. In Fred Brackx, H. De Schepper, & J. Van der Jeugt (Eds.), Journal of Physics : Conference Series (Vol. 597). Presented at the 30th International colloquium on Group Theoretical Methods in Physics (ICGTMP), Bristol, UK: IOP.
Vancouver
1.
De Bie H, Oste R, Van der Jeugt J. Unique characterization of the Fourier transform in the framework of representation theory. In: Brackx F, De Schepper H, Van der Jeugt J, editors. Journal of Physics : Conference Series. Bristol, UK: IOP; 2015.
MLA
De Bie, Hendrik, Roy Oste, and Joris Van der Jeugt. “Unique Characterization of the Fourier Transform in the Framework of Representation Theory.” Journal of Physics : Conference Series. Ed. Fred Brackx, Hennie De Schepper, & Joris Van der Jeugt. Vol. 597. Bristol, UK: IOP, 2015. Print.