Abstract
The inverse problem for the discrete analogue of the exterior transmission eigenvalue problem with a spherically symmetric index of refraction is considered. For the absorbing media, we show that the index of refraction can be recovered uniquely if all the exterior transmission eigenvalues (counting with their multiples) are given together with partial information on the entries of the index of refraction. Meanwhile, for the non-absorbing media, we obtain that exterior transmission eigenvalues can completely determine the index of refraction.
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