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Journal d'Analyse Mathématique

, Volume 133, Issue 1, pp 1–25 | Cite as

Singularities of the wave trace for the Friedlander model

  • Yves Colin de Verdière
  • Victor Guillemin
  • David Jerison
Article
  • 64 Downloads

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 2πε < 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.

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Copyright information

© Hebrew University Magnes Press 2017

Authors and Affiliations

  • Yves Colin de Verdière
    • 1
  • Victor Guillemin
    • 2
  • David Jerison
    • 2
  1. 1.Institut FourierUnité Mixte De Recherche Cnrs-Ujf 5582Saint Martin d’Hères CedexFrance
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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