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We study an inverse uniqueness with a knowledge of spectral data in theinterior transmission problem defined by an index of refraction in a simpledomain. We expand the solution in such a domain into a series of onedimensional problems. For each one dimensional problem, we apply a valuedistribution theory in complex analysis to describe the eigenvalues of thesystem. By the orthogonality of the one dimensional system, we consider theuniqueness on the perturbation along each given incident angle.

An Inverse Uniqueness in Interior Transmission Problem and Its Eigenvalue Tunneling in Penetrable Simple Domains