Stability in the inverse nodal solution for the interior transmission problem

The inverse nodal problem of determining a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from zeros for eigenfunctions corresponding to the transmission eigenvalues. It is shown that the space of potential functions q   which correspond to interior transmission problems characterized by Ω:={q:q∈L2[0,1]}Ω:={q:q∈L2[0,1]}, under a certain metric, is homeomorphic to the partition set of the space of quasinodal sequences. As a consequence, the inverse nodal problem defined on the partition set of admissible sequence, is stable.