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The radiation field is a Fourier integral operator. (English) Zbl 1091.58018
Authors’ 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.

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
35L05 Wave equation
35P25 Scattering theory for PDEs
58J45 Hyperbolic equations on manifolds
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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