Recovering asymptotics of metrics from fixed energy scattering data
Antônio Sá Barreto, Mark Joshi
Abstract
The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on Rn from fixed energy scattering data is studied. It is shown that if two such metrics, g1, g2, have scattering data at some fixed energy which are equal up to smoothing, then there exists a diffeomorphism ψ`fixing infinity' such that ψ*(g1) - g2 is rapidly decreasing. Given the scattering matrix at two energies, it is shown that the asymptotics of a metric and a short range potential can be determined simultaneously. These results also hold for a wide class of scattering manifolds.
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