Singularities of the wave trace for the Friedlander model

In a recent preprint, [CGJ], we showed that for the Dirichlet Laplacian ∆ on the unit disk, the wave trace Tr(eit √ ∆), which has complicated singularities on 2π − ε < t < 2π, is, on the interval 2π < t < 2π+ ε, the restriction to this interval of a C∞ function on its closure. In this paper we prove the analogue of this somewhat counter-intuitive result for the Friedlander model. The proof for the Friedlander model is simpler and more transparent than in the case of the unit disk.