On the dual of a commutative signed hypergroup

Signed hypergroups are convolution structures similar to hypergroups, though being not necessarily positivity-preserving. We prove a generalized Plancherel theorem for positive definite measures on a commutative signed hypergroup, with an analogue of the classical Plancherel theorem as a special case. Moreover, signed hypergroups with subexponential growth are studied. As an application, the dual of the Laguerre convolution structure on ℝ₊ is determined.