Inverse spectral analysis for the transmission eigenvalue problem

The uniqueness problem of determining a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of the transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. Let a denote the integral of 1/v on the interval [0, b]. If a = b then v is uniquely determined by the data consisting of all the transmission eigenvalues plus an appropriate value of v or its derivative at the endpoint b. If a > b, the unique recovery is obtained by the data consisting of all the transmission eigenvalues together with the normalizing constants corresponding to the partial simple eigenvalues.