no. 2
A sharp lower bound for a resonance-counting function in even dimensions
[Minoration optimale de la fonction de comptage des résonances en dimension paire]
Christiansen, T. J.1
1 Department of Mathematics University of Missouri 202 Math Science Building Columbia, MO 65211 (USA)
Annales de l'Institut Fourier, Tome 67 (2017) no. 2, pp. 579-604.

L’objet de cette note est de montrer des bornes inférieures optimales pour la fonction de comptage des résonances, dans le cas d’obstacles sur l’espace euclidien en dimension paire ; on ne fait aucune hypothèse de capture du flot de billard extérieur à l’obstacle. Des minorations similaires sont prouvées pour d’autres types de perturbations à support compact sur ℝ d . La preuve utilise une formule de Poisson pour les résonances, complémentaire d’une formule montrée par Zworski en dimension paire.

This paper proves sharp lower bounds on a resonance-counting function for obstacle scattering in even-dimensional Euclidean space without a need for trapping assumptions. Similar lower bounds are proved for some other compactly supported perturbations of -Δ on ℝ d , for example, for the Laplacian for certain metric perturbations on ℝ d . The proof uses a Poisson formula for resonances, complementary to one proved by Zworski in even dimensions.

Reçu le :
Révisé le :
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DOI : 10.5802/aif.3092
Classification : 35P25, 58J50, 35P20, 47A40
Keywords: scattering theory, resonance, obstacle, metric
Mot clés : théorie de la diffusion, résonance, obstacle, métrique
Christiansen, T. J. 1

1 Department of Mathematics University of Missouri 202 Math Science Building Columbia, MO 65211 (USA)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Christiansen, T. J. A sharp lower bound for a resonance-counting function in even dimensions. Annales de l'Institut Fourier, Tome 67 (2017) no. 2, pp. 579-604. doi : 10.5802/aif.3092. https://aif.centre-mersenne.org/articles/10.5802/aif.3092/

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