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The radiation field is a Fourier integral operator

Antônio Sá Barreto, Jared Wunsch (2005)

Annales de l’institut Fourier

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...

The resolvent for Laplace-type operators on asymptotically conic spaces

Andrew Hassell, András Vasy (2001)

Annales de l’institut Fourier

Let X be a compact manifold with boundary, and g a scattering metric on X , which may be either of short range or “gravitational” long range type. Thus, g gives X the geometric structure of a complete manifold with an asymptotically conic end. Let H be an operator of the form H = Δ + P , where Δ is the Laplacian with respect to g and P is a self-adjoint first order scattering differential operator with coefficients vanishing at ∂ X and satisfying a “gravitational” condition. We define a symbol calculus for...

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