[Le champs de radiation est un opérateur intégral de Fourier]
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.
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.
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
@article{AIF_2005__55_1_213_0,
author = {S\'a Barreto, Ant\^onio and Wunsch, Jared},
title = {The radiation field is a {Fourier} integral operator},
journal = {Annales de l'Institut Fourier},
pages = {213--227},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {55},
number = {1},
year = {2005},
doi = {10.5802/aif.2096},
mrnumber = {2141696},
zbl = {1091.58018},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2096/}
}
TY - JOUR AU - Sá Barreto, Antônio AU - Wunsch, Jared TI - The radiation field is a Fourier integral operator JO - Annales de l'Institut Fourier PY - 2005 SP - 213 EP - 227 VL - 55 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2096/ DO - 10.5802/aif.2096 LA - en ID - AIF_2005__55_1_213_0 ER -
%0 Journal Article %A Sá Barreto, Antônio %A Wunsch, Jared %T The radiation field is a Fourier integral operator %J Annales de l'Institut Fourier %D 2005 %P 213-227 %V 55 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2096/ %R 10.5802/aif.2096 %G en %F AIF_2005__55_1_213_0
Sá Barreto, Antônio; Wunsch, Jared. The radiation field is a Fourier integral operator. Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 213-227. doi : 10.5802/aif.2096. http://www.numdam.org/articles/10.5802/aif.2096/
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