The radiation field is a Fourier integral operator
Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 213-227.

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.

On démontre que pour toute variété non-captive asymptotiquement hyperbolique ou asymptotiquement conique, le champs de radiation introduit par F.G. Friedlander qui est l'opérateur envoyant la donnée de Cauchy pour l'équation des ondes sur l'asymptotique rééchelonné de l'onde, est un opérateur intégral de Fourier. La relation canonique sous- jacente est associée au temps de séjour, ou fonction de Busemann, des géodésiques. Comme conséquence, on obtient des informations sur le comportement à haute fréquence de l'opérateur de Poisson dans ces cadres géométriques.

DOI: 10.5802/aif.2096
Classification: 35L05, 35P25, 58J40, 58J45, 58J50
Keywords: Radiation field, sojourn time, Busemann function, high frequency, Eisenstein function
Mot clés : champs de radiation, temps de séjour, fonction de Busemann, haute fréquence, fonction Eisenstein
Sá Barreto, Antônio 1; Wunsch, Jared 

1 Purdue University, Department of Mathematics, 150 North University Street, West Lafayette IN 47907 (USA), Northwestern University, Department of Mathematics, 2033 Sheridan Rd., Evanston IL 60208 (USA)
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Sá Barreto, Antônio; Wunsch, Jared. The radiation field is a Fourier integral operator. Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 213-227. doi : 10.5802/aif.2096. https://aif.centre-mersenne.org/articles/10.5802/aif.2096/

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