Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-03-10
Commun.Math.Phys. 204 (1999) 397-423
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages, 2 figures, submitted to Comm. Math. Phys
Scientific paper
10.1007/s002200050651
The completeness of the quasinormal modes of the wave equation with Poeschl-Teller potential is investigated. A main result is that after a large enough time $t_0$, the solutions of this equation corresponding to $C^{\infty}$-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 $t_0$ 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.
Beyer Horst R.
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