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Trace formulae, resonances and quasi-modes (after Sjöstrand-Zworski, Stefanov-Vodev et al.). (Formules de trace, résonances et quasi-modes (d’après Sjöstrand-Zworski, Stefanov-Vodev et al.).) (French) Zbl 1049.35121

Séminaire Bourbaki. Volume 1998/99. Exposés 850–864. Paris: Société Mathématique de France. Astérisque 266, 175-191, Exp. No. 856 (2000).
Summary: The purpose of this talk is to present recent results about the existence of resonances (for Laplace operators in the exterior of an obstacle or Schrödinger operators). We present on the one hand trace formulas recently established by J. Sjöstrand et M. Zworski and some applications and on the other some results by P. Stefanov, G. Vodev, S.H. Tang and M. Zworski showing that the constructions of quasi-modes known for years, allow now to prove the existence of resonances near these quasi-modes.
For the entire collection see [Zbl 0939.00019].

MSC:

35L05 Wave equation
35P25 Scattering theory for PDEs
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