Continuous Gabor transform for strong hypergroups

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.