Generalized Fourier Transforms Associated with the Oscillator Representation

  • Jing-Song HuangEmail author
  • Ling Zhou
Research Article


By identifying the Fourier transform \(\mathcal {F}\) with an operator in the oscillator representation of the metaplectic group \({\widetilde{Sp}(2n,\mathbb {R})}\), the twofold cover of the symplectic group \(Sp(2n,\mathbb {R})\), we study generalized Fourier transforms inspired by the work of De Bie, Oste and Van der Jeugt. We obtain several families of operators \(\mathcal {T}\)’s that have the important properties similar to \(\mathcal {F}\) using various dual pair correspondences.


Fourier transform Oscillator representation Dual pair correspondence 



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Authors and Affiliations

  1. 1.Department of MathematicsHong Kong University of Science and TechnologyKowloonChina
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA

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