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.

Continuous Gabor transform for strong hypergroups

GIGANTE, Giacomo;
2003-01-01

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.
journal article - articolo
2003
Gigante, Giacomo; Czaja, Wojciech
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/24771
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