On Schrödinger operators with ${\delta }^{\mathrm{\prime }}$-potentials supported on star graphs

The spectral properties of two-dimensional Schrödinger operators with ${\delta }^{\mathrm{\prime }}$-potentials supported on star graphs are discussed. We describe the essential spectrum and give a complete description of situations in which the discrete spectrum is non-trivial but finite. A more detailed study is presented for the case of a star graph with two branches, in particular, the small angle asymptotics for the eigenvalues is obtained.