The inverse interior transmission eigenvalue problem with mixed spectral data

Abstract

The inverse spectral problem for the interior transmission eigenvalue problem with the unit time is studied by given spectral data. The authors show that the refractive index on the whole interval can be uniquely determined by parts of its transmission eigenvalues together with the partial information on the refractive index. In particular, we pose and solve a new type of inverse spectral problems involving the interior transmission eigenvalue problem with complex transmission eigenvalues except for at most finite real eigenvalues.