Singularities of the wave trace for the Friedlander model

Abstract

In a recent preprint, we showed that for the Dirichlet Laplacian $\Delta$ on the unit disk, the wave trace $Tr(e^{it\sqrt{\Delta }})$, which has complicated singularities on $2\pi -\epsilon <t<2\pi$, is, on the interval $2\pi <t<2\pi +\epsilon$, 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.