The scattering operator on asymptotically hyperbolic manifolds

The scattering operator on asymptotically hyperbolic manifolds

We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the forward fundamental solution of the wave operator on asymptotically hyperbolic manifolds. This formula is then used to show that the scattering operator is a Fourier integral operator that q...

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Veröffentlicht in:Journal of spectral theory 2019-01, Vol.9 (1), p.269-313
Hauptverfasser: Sá Barreto, Antônio, Wang, Yiran
Format: Artikel
Sprache:eng
Schlagworte:
Global analysis, analysis on manifolds
Novels
Partial differential equations
Radiation (Physics)
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Beschreibung
Zusammenfassung:We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the forward fundamental solution of the wave operator on asymptotically hyperbolic manifolds. This formula is then used to show that the scattering operator is a Fourier integral operator that quantizes the scattering relation.
ISSN:1664-039X
1664-0403
DOI:10.4171/JST/248