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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)
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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.
Keywords
Generalized Fourier Transform

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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.
@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},
}

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