Speaker:
Horst Beyer,
Max Planck Institute for Gravitational Physics, Golm, Germany,
and Dept. of Mathematics, LSU
Title:
On the Completeness of the Resonance Modes of the Poschl-Teller Potential
Abstract:
The completeness of the resonance (or quasinormal) modes of the wave
equation with Poschl-Teller potential is investigated. A main result
is that, after a large enough time t0, the solutions of this equation
corresponding to C-infinite data with compact support can be expanded
uniformly in time with respect to the quasinormal modes, thereby
leading to absolutely convergent series. Explicit estimates for t0
depending on both the support of the data and the point of observation
are given. For the particular case of an "early" time and zero
distance between the support of the data and observational point,
it is shown that the corresponding series is not absolutely convergent,
and hence that there is no associated sum which is independent of the
order of summation. The relevance of the results for the resonance modes
of spherically symmetric (Schwarzschild) black holes is discussed.