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

30th International Colloquium on Group Theoretical Methods in Physics

De Bie, H.^1 ; Oste, R.^2 ; Van Der Jeugt, J.^2

Department of Mathematical Analysis, Faculty of Engineering and Architecture - Ghent University, Galglaan 2, 9000 Gent, Belgium^1

Department of Applied Mathematics Computer Science and Statistics, Faculty of Sciences, Ghent University, Krijgslaan 281, Gent

9000, Belgium^2

关键词: Dual pairs;    Lie Algebra;    Representation theory;    Symmetry properties;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012026/pdf
DOI  :  10.1088/1742-6596/597/1/012026

来源: IOP

【 摘 要 】

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),sl2). We prove in detail a result on the unique characterization of the FT making extensive use of a representation of the Lie algebra sl2. 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.