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The Lagrangian Radon Transform and the Weil Representation

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Abstract

We consider the operator \(\mathcal {R}\), which sends a function on \({\mathbb {R}}^{2n}\) to its integrals over all affine Lagrangian subspaces in \({\mathbb {R}}^{2n}\). We discuss properties of the operator \(\mathcal {R}\) and of the representation of the affine symplectic group in several function spaces on \({\mathbb {R}}^{2n}\).

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Authors and Affiliations

  1. Dipartimento di Fisica, Universitá di Napoli Federico II and INFN, Sezione di Napoli, Via Cintia, 80126 , Napoli, Italy

    Giuseppe Marmo

  2. Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 , Wien, Austria

    Peter W. Michor & Yury A. Neretin

  3. Institute for Theoretical and Experimental Physics, Moscow, Russia

    Yury A. Neretin

  4. MechMath Department, Moscow State University, Moscow, Russia

    Yury A. Neretin

Authors
  1. Giuseppe Marmo
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  2. Peter W. Michor
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  3. Yury A. Neretin
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Corresponding author

Correspondence to Peter W. Michor.

Additional information

Communicated by Karlheinz Gröchenig.

YuAN was supported by FWF Projects P 22122 and P 25142.

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Marmo, G., Michor, P.W. & Neretin, Y.A. The Lagrangian Radon Transform and the Weil Representation. J Fourier Anal Appl 20, 321–361 (2014). https://doi.org/10.1007/s00041-013-9315-0

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  • DOI: https://doi.org/10.1007/s00041-013-9315-0

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