The uniqueness for inverse discrete exterior transmission eigenvalue problems in spherically symmetric media

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.

Keywords:

• Inverse scattering
• exterior transmission eigenvalues
• inverse spectral problem
• discrete version

2010 Mathematics Subject Classifications:

• 15A29
• 34A55

Acknowledgments

We would like to thank the referees for a very careful reading of our manuscript and for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).