Singularities of the wave trace for the Friedlander model

In a recent preprint, we showed that for the Dirichlet Laplacian $Δ$ on the unit disk, the wave trace ${Tr}(e^{it\sqrtΔ})$, which has complicated singularities on $2π- ε< t < 2π$, is, on the interval $2π< t < 2π+ ε$, the restriction to this interval of a $C^\infty$ 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.

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