no. 3
Estimates on the number of scattering poles near the real axis for strictly convex obstacles
Annales de l'Institut Fourier, Tome 43 (1993) no. 3, pp. 769-790.

Pour le laplacien de Dirichlet de l’extérieur d’un obstacle strictement convexe, nous montrons que le nombre de pôles de scattering de module ≤r dans un angle θ près de l’axe réel, peut être majoré par Constθ 3/2 r n pour r assez grand dépendant de θ. Ici n est la dimension.

For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus ≤r in a small angle θ near the real axis, can be estimated by Const θ 3/2 r n for r sufficiently large depending on θ. Here n is the dimension.

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     title = {Estimates on the number of scattering poles near the real axis for strictly convex obstacles},
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Sjöstrand, Johannes; Zworski, Maciej. Estimates on the number of scattering poles near the real axis for strictly convex obstacles. Annales de l'Institut Fourier, Tome 43 (1993) no. 3, pp. 769-790. doi : 10.5802/aif.1355. https://aif.centre-mersenne.org/articles/10.5802/aif.1355/

[M1] R. Melrose, Polynomial bounds on the number of scattering poles, J. Funct. An., 53 (1983), 287-303. | MR | Zbl

[M2] R. Melrose, Polynomial bounds on the distribution of poles in scattering by an obstacle, Journées équations aux dérivées partielles, Saint Jean de Monts (1984) (published by Centre de Mathématiques, École Polytechnique, Palaiseau, France). | EuDML | Numdam | Zbl

[R] D. Robert, Autour de l'approximation semi-classique, Progress in Math., vol. 68, Birkhäuser (1987). | MR | Zbl

[O] F.W.J. Olver, The asymptotic expansions of Bessel functions of large order, Phil. Trans. Roy. Soc. London, Ser. A, 247 (1954), 328-368. | MR | Zbl

[S] J. Sjöstrand, Geometric bounds on the density of resonances for semi-classical problems, Duke Mathematical Journal, 61 (1) (1990), 1-57. | MR | Zbl

[SZ1] J. Sjöstrand, M. Zworski, Complex scaling and the distribution of scattering poles, Journal of the AMS, 4 (4) (1991), 729-769. | MR | Zbl

[SZ2] J. Sjöstrand, M. Zworski, Distribution of scattering poles near the real axis, Comm. P.D.E., 17 (5 & 6) (1992), 1021-1035. | MR | Zbl

[V] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys., 146 (1992), 205-216. | MR | Zbl

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