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Radiation fields on asymptotically Euclidean manifolds. (English) Zbl 1037.58020
Summary: F. G. Friedlander [Math. Proc. Cambridge Phil. Soc. 88, 483–515 (1980; Zbl 0405.35068), J. Funct. Anal. 184, 1–18 (2001; Zbl 0997.58013)] introduced the notion of radiation fields for asymptotically Euclidean manifolds. Here we answer some of the questions he proposed and apply the results to give a unitary translation representation of the wave group, and to obtain the scattering matrix for such manifolds. We also obtain a support theorem for the radiation fields.

MSC:
58J45 Hyperbolic equations on manifolds
44A12 Radon transform
81U20 \(S\)-matrix theory, etc. in quantum theory
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
35P25 Scattering theory for PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
78A40 Waves and radiation in optics and electromagnetic theory
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