Uncertainty principles for the Heckman-Opdam transform (Q310069)

This paper is concerned with analogues of classical uncertainty principles in the framework of hypergeometric harmonic analysis in root systems, where an uncertainty principle is a statement of the form that a function and its Fourier transform cannot both be `small'. `Being small' is quantified in terms of entropy, which is more reasonable from the viewpoint of the quantum mechanics.NEWLINENEWLINEThe author establishes several uncertainty principles for the Heckman-Opdam `hypergeometric' Fourier transform associated with a root system of arbitrary rank, including analogues of 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.