Uncertainty principles for the Heckman–Opdam transform

We establish several uncertainty principles for the Heckman–Opdam ‘hypergeometric’ Fourier transform associated with a root system of arbitrary rank, including analogues of the Donoho–Stark and Benedicks–Amrein–Berthier principles, and the Hirschman entropic uncertainty inequality. For rank one root systems, these results hold more generally for the Cherednik–Opdam transform.