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Continuous Gabor Transform for Strong Hypergroups

  • Wojciech Czaja
  • Giacomo Gigante
Article

Abstract

We define a continuous Gabor transform for strong hypergroups and prove a Plancherel formula, an L 2 inversion formula and an uncertainty principle for it. As an example, we show how these techniques apply to the Bessel–Kingman hypergroups and to the dual Jacobi polynomial hypergroups. These examples have an interpretation in the setting of radial functions on R d and zonal functions on compact two-point homogeneous spaces, where they provide a new transform which possesses many properties of the classical Gabor transform.

Keywords

Homogeneous Space Uncertainty Principle Radial Function Inversion Formula Zonal Function 
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Copyright information

© Birkhauser Boston 2003

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of Wroclaw, pl. Grunwaldzki 2/4, 50-384 WroclawPoland
  2. 2.Department of MathematicsUniversity of Maryland, College Park, MD 20742-4015USA
  3. 3.Dipartimento di IngegneriaUniversità degli Studi di Bergamo, Viale Marconi, 5, 24044 Dalmine (BG)Italy

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