Recovering singularities of a potential from singularities of scattering data |
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| Authors: | Allan Greenleaf Gunther Uhlmann |
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| Affiliation: | (1) Department of Mathematics, University of Rochester, 14627 Rochester, New York, USA;(2) Department of Mathematics, University of Washington, 98195 Seattle, Washington, USA |
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| Abstract: | 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.Partially supported by NSF Grant DMS-9101298 and an Alfred P. Sloan Research FellowshipPartially supported by NSF Grant DMS-9100178 |
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