Summary: This note is devoted to the spectral analysis of an unbounded operator associated with a noncoercive transmission problem. Using an integral equation method, we show that, if the interface is regular, this operator is selfadjoint and has compact resolvent. If the interface has a corner, the study of the singularities using Mellin transform allows us to derive a necessary and sufficient condition on the contrast between the two media for selfadjointness. If the operator is not selfadjoint, a characterization of its selfadjoint extensions is given.