Singularities of the wave trace for the Friedlander model

Abstract

In a recent preprint, we showed that for the Dirichlet Laplacian Δ on the unit disk, the wave trace $$Tr\left( {{e^{it\sqrt \Delta }}} \right)$$ , which has complicated singularities on 2π−e < t < 2π, is bounded and infinitely differentiable as t →2π from the right. 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 and suggests the direction to follow to treat the case of general smooth strictly convex domains.