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Radiation fields, scattering and inverse scattering on asymptotically hyperbolic manifolds
, 2004
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SCATTERING AND INVERSE SCATTERING ON ACH MANIFOLDS
, 2006
"... We study scattering and inverse scattering theories for asymptotically complex hyperbolic manifolds. We show the existence of the scattering operator as a meromorphic family of operators in the Heisenberg calculus on the boundary, which is a contact manifold with a pseudohermitian structure. Then ..."
Abstract

Cited by 7 (1 self)
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We study scattering and inverse scattering theories for asymptotically complex hyperbolic manifolds. We show the existence of the scattering operator as a meromorphic family of operators in the Heisenberg calculus on the boundary, which is a contact manifold with a pseudohermitian structure. Then we define radiation fields as in the real asymptotically hyperbolic case, and reconstruct the scattering operator from those fields. As an application we show that the manifold, including its topology and the metric, are determined up to invariants by the scattering matrix at all energies.
CORRESPONDENCES AND INDEX
, 2008
"... We define certain class of correspondences of polarized representations of C ∗algebras. Our correspondences are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In this setup we define the index. The main subject of the paper is the additivity of the ..."
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We define certain class of correspondences of polarized representations of C ∗algebras. Our correspondences are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In this setup we define the index. The main subject of the paper is the additivity of the index. 1