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Note on a Uniqueness Theorem of Schiffer
Authors:D Colton  B D Sleeman  B D Sleeman
Institution:1. Department of Mathematics , Ohio University , Athens, OH, 45701;2. Department of Mathematics , Bandung Institute of Technology Ganesha 10 , Bandung, Indonesia
Abstract:AMS (MOS): 35R30, 76Q05

The uniqueness of the inverse scattering problem is examined. It is shown that the boundary conditions must be suitably restricted to secure uniqueness. For one class the far-field pattern for one incident field is sufficient for uniqueness and, for a wider class, information from a finite number of distinct incident waves suffices. In either case, the far-field also dictates the boundary condition on the scatterer.
Keywords:34K05  34K15  58F13  58F14
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