The radiation field is a Fourier integral operator

Antônio Sá Barreto[1]; Jared Wunsch

  • [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)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 1, page 213-227
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Sá Barreto, Antônio, and Wunsch, Jared. "The radiation field is a Fourier integral operator." Annales de l’institut Fourier 55.1 (2005): 213-227. <http://eudml.org/doc/116186>.

@article{SáBarreto2005,
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.},
affiliation = {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)},
author = {Sá Barreto, Antônio, Wunsch, Jared},
journal = {Annales de l’institut Fourier},
keywords = {Radiation field; sojourn time; Busemann function; high frequency; Eisenstein function; radiation field},
language = {eng},
number = {1},
pages = {213-227},
publisher = {Association des Annales de l'Institut Fourier},
title = {The radiation field is a Fourier integral operator},
url = {http://eudml.org/doc/116186},
volume = {55},
year = {2005},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 1
SP - 213
EP - 227
AB - 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.
LA - eng
KW - Radiation field; sojourn time; Busemann function; high frequency; Eisenstein function; radiation field
UR - http://eudml.org/doc/116186
ER -

References

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