| Abstract: |
| We consider the uniqueness question for the inverse modified transmission eigenvalue problem from modified transmission eigenvalues. We assume that the refractive index is spherically symmetric and piecewise continuous. The corresponding direct spectral transmission problem refers to a system of two Helmholtz type equations in the same domain where the spectral parameter appears in the one equation, which corresponds to an artificial metamaterial. In addition, the two corresponding fields have equal Cauchy data on the boundary. By using separation of variables to describe the direct problem, we reconstruct the Dirichlet-to-Neumann map for the field that satisfies the Helmholtz equation with the refractive index n(r). By utilizing well-known results from the Borg-Levinson theory for Schrodingers equation we prove the uniqueness of the recovery of n(r). We explore some special properties of the spectrum and present simple examples. |
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