The scattering operator on asymptotically hyperbolic manifolds

Antônio Sá Barreto; Yiran Wang

doi:10.4171/jst/248

JournalsjstVol. 9, No. 1pp. 269–313

The scattering operator on asymptotically hyperbolic manifolds

Antônio Sá Barreto
Purdue University, West Lafayette, USA
Yiran Wang
University of Washington, Seattle, USA and The Hong Kong University of Science and Technology, Hong Kong
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Abstract

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.

Cite this article

Antônio Sá Barreto, Yiran Wang, The scattering operator on asymptotically hyperbolic manifolds. J. Spectr. Theory 9 (2019), no. 1, pp. 269–313

DOI 10.4171/JST/248