Abstract
We show that the "radiation field" introduced by F.G. Friedlander, mapping Cauchy data for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic manifold. The underlying canonical relation is associated to a "sojourn time" or "Busemann function" for geodesics. As a consequence we obtain some information about the high frequency behavior of the scattering Poisson operator in these geometric settings.
Original language | English (US) |
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Pages (from-to) | 213-227+VII+XI |
Journal | Annales de l'Institut Fourier |
Volume | 55 |
Issue number | 1 |
DOIs | |
State | Published - 2005 |
Keywords
- Busemann function
- Eisenstein function
- High frequency
- Radiation field
- Sojourn time
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology