Transmission eigenvalues for multipoint scatterers

We study the transmission eigenvalues for the multipoint scatterers of the Bethe–Peierls–Fermi–Zeldovich–Beresin–Faddeev type in dimensions $d = 2$ and $d = 3$. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension $d = 1$ is also discussed.