Translator Disclaimer
15 September 2005 Radiation fields, scattering, and inverse scattering on asymptotically hyperbolic manifolds
Antônio Sá Barreto
Author Affiliations +
Duke Math. J. 129(3): 407-480 (15 September 2005). DOI: 10.1215/S0012-7094-05-12931-3

Abstract

We define the forward and backward radiation fields on an asymptotically hyperbolic manifold and show that they give unitary translation representations of the wave group and as such can be used to define a scattering matrix. We show that this scattering matrix is equivalent to the one defined by stationary methods. Furthermore, we prove a support theorem for the radiation fields which generalizes to this setting well-known results of Helgason [23] and Lax and Phillips [35] for the horocyclic Radon transform. As an application, we use the boundary control method of Belishev [4] to show that an asymptotically hyperbolic manifold is determined up to invariants by the scattering matrix at all energies.

Citation

Download Citation

Antônio Sá Barreto. "Radiation fields, scattering, and inverse scattering on asymptotically hyperbolic manifolds." Duke Math. J. 129 (3) 407 - 480, 15 September 2005. https://doi.org/10.1215/S0012-7094-05-12931-3

Information

Published: 15 September 2005
First available in Project Euclid: 19 October 2005

zbMATH: 1154.58310
MathSciNet: MR2169870
Digital Object Identifier: 10.1215/S0012-7094-05-12931-3

Subjects:
Primary: 81U40
Secondary: 35P25

Rights: Copyright © 2005 Duke University Press

JOURNAL ARTICLE
74 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.129 • No. 3 • 15 September 2005
Back to Top