A local two radii theorem on the Chébli–Trimèche hypergroup

Abstract Let 0 r 1 r 2 r 1 + r 2 R . It is given a necessary and sufficient condition so that the null function is the unique solution f ∈ C ∞ ( ] − R , + R [ ) of the system (1) ∫ 0 + r i T x f ( y ) A ( y ) d y = 0 , | x | R − r i , i = 1 , 2 , where A ( y ) d y is the Haar measure and T x is the x -translation operator on the Chebli–Trimeche hypergroup. The result obtained is especially available for Bessel–Kingmann and Jacobi hypergroups.