The radiation field is a Fourier integral operator

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.

Locations

• arXiv (Cornell University) - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF
• French digital mathematics library (Numdam) - View - PDF
• Annales de l’institut Fourier - View - PDF