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Density of Resonances for Strictly Convex Analytic Obstacles

Published online by Cambridge University Press:  20 November 2018

Johannes Sjöstrand
Johannes Sjöstrand*
Affiliation:
Centre de Mathématiques Ecole Polytechnique F-91128 Palaiseau Cedex France
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Abstract

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We estimate the density of resonances close to a critical curve, for strictly convex obstacles with analytic boundary. Contrary to the C∞-case, already treated with Zworski, the estimates are in terms of dynamical quantities. A new feature in the proof is a certain averaging procedure.

Résumé

Résumé

Nous estimons la densité des résonances près d'une courbe critique, pour des obstacles strictement convexes à bord analytique. Contrairement au cas C∞, déjà traité avec Zworski, les estimations font appel aux quantités dynamiques. Une procédure de moyennisation est un aspect nouveau dans la demonstration.

Keywords

35L2035A2235A2735P2535P26resonanceFBI-transform
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 2 , 01 April 1996 , pp. 397 - 447
Copyright
Copyright © Canadian Mathematical Society 1996

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