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Density of resonances for strictly convex analytic obstacles. With an appendix by M. Zworski. (English) Zbl 0863.35072

The author estimates the density of resonances close to a critical curve, for strictly convex obstacles with analytic boundary. Contrary to the \(C^\infty\) case, already treated in [the author and M. Zworski, [1] Ann. Inst. Fourier 43, No. 3, 769-790 (1993; Zbl 0784.35073) and [2] Ark. Mat. 33, No. 1, 135-172 (1995; Zbl 0839.35095)], the estimates are in terms of dynamical quantities. The appendix of Zworski is devoted to some improvement of [2] based on the techniques presented in the paper under review.
Reviewer: B.Helffer (Orsay)

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35P25 Scattering theory for PDEs

Keywords:

critical curve
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