On the completeness of the quasinormal modes of the Poschl-Teller potential

The completeness of the quasinormal modes of the wave equation with Poschl- Teller potential is investigated, A main result is that after a large enoug h time t(0), the solutions of this equation corresponding to C-infinity-dat a with compact support can be expanded uniformly in time with respect to th e quasinormal modes, thereby leading to absolutely convergent series. Expli cit estimates for t(0) depending on both the support of the data and the po int of observation are given. For the particular case of an "early" time an d zero distance between the support of the data and observational point, it is shown that the corresponding series is riot absolutely convergent, and hence that there is no associated sum which is independent of the order of summation.