Recovering singularities of a potential from singularities of scattering data
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- Greenleaf, A. & Uhlmann, G. Commun.Math. Phys. (1993) 157: 549. doi:10.1007/BF02096882
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In this paper we show that the leading singularities of certain potentials can be determined from the leading singularities of the backscattering (as well as other determined sets of scattering data). The potentials in question are conormal with respect to smooth surfaces of arbitrary dimension; the restrictions on their orders allow for unbounded potentials in all dimension greater than or equal to three.