Abstract
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.
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Communicated by Hans G. Feichtinger.
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Jing-Song Huang: research is supported by research Grants from the Research Grant Council of Hong Kong SAR in China.
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Huang, JS., Zhou, L. Generalized Fourier Transforms Associated with the Oscillator Representation. J Fourier Anal Appl 25, 2782–2800 (2019). https://doi.org/10.1007/s00041-019-09682-0
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DOI: https://doi.org/10.1007/s00041-019-09682-0