The radiation field is a fourier integral operator

Antônio Sá. Barreto*, Jared Wunsch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)213-227+VII+XI
JournalAnnales de l'Institut Fourier
Volume55
Issue number1
DOIs
StatePublished - 2005

Keywords

  • Busemann function
  • Eisenstein function
  • High frequency
  • Radiation field
  • Sojourn time

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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