The scattering operator on asymptotically hyperbolic manifolds

2016/09/08 by Antônio Sá Barreto, Yiran Wang, Barreto, Antônio Sá +1
Mathematics · #35P25 #58J50 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1609.02332

openalex publication_date 2016/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the fundamental solution of the wave operator on asymptotically hyperbolic manifolds. If there are no trapped geodesics, this formula is used to show that the scattering operator is a Fourier integral operator that quantizes the scattering relation.

Related

• Scattering and Inverse Scattering on ACH Manifolds
• The wave kernel on asymptotically complex hyperbolic manifolds
• Inverse Scattering on Asymptotically Hyperbolic Manifolds
• Higher order scattering on asymptotically Euclidean Manifolds
• The Scattering Relation on Asymptotically Hyperbolic Manifolds