Journal of Fourier Analysis and Applications

, Volume 20, Issue 2, pp 321–361 | Cite as

The Lagrangian Radon Transform and the Weil Representation

  • Giuseppe Marmo
  • Peter W. Michor
  • Yury A. Neretin
Article

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 \({\mathbb {R}}^{2n}\).

Keywords

Radon transform Symplectic group Weil representation Siegel half-plane Intertwining operators Invariant differential operators Fourier transform 

Mathematics Subject Classification

44A12 46F12 35E99 22E46 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Giuseppe Marmo
    • 1
  • Peter W. Michor
    • 2
  • Yury A. Neretin
    • 2
    • 3
    • 4
  1. 1.Dipartimento di FisicaUniversitá di Napoli Federico II and INFN, Sezione di NapoliNapoliItaly
  2. 2.Fakultät für MathematikUniversität WienWienAustria
  3. 3.Institute for Theoretical and Experimental PhysicsMoscowRussia
  4. 4.MechMath DepartmentMoscow State UniversityMoscowRussia

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