Geodesic
Density of Resonances for Strictly Convex Analytic Obstacles
Canadian journal of mathematics, Tome 48 (1996) no. 2, pp. 397-447

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1996-022-9
Mots-clés : 35L20, 35A22, 35A27, 35P25, 35P26, resonance, FBI-transform 
Sjöstrand, Johannes. Density of Resonances for Strictly Convex Analytic Obstacles. Canadian journal of mathematics, Tome 48 (1996) no. 2, pp. 397-447. doi: 10.4153/CJM-1996-022-9
@article{10_4153_CJM_1996_022_9,
     author = {Sj\"ostrand, Johannes},
     title = {Density of {Resonances} for {Strictly} {Convex} {Analytic} {Obstacles}},
     journal = {Canadian journal of mathematics},
     pages = {397--447},
     year = {1996},
     volume = {48},
     number = {2},
     doi = {10.4153/CJM-1996-022-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-022-9/}
}
TY  - JOUR
AU  - Sjöstrand, Johannes
TI  - Density of Resonances for Strictly Convex Analytic Obstacles
JO  - Canadian journal of mathematics
PY  - 1996
SP  - 397
EP  - 447
VL  - 48
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-022-9/
DO  - 10.4153/CJM-1996-022-9
ID  - 10_4153_CJM_1996_022_9
ER  - 
%0 Journal Article
%A Sjöstrand, Johannes
%T Density of Resonances for Strictly Convex Analytic Obstacles
%J Canadian journal of mathematics
%D 1996
%P 397-447
%V 48
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-022-9/
%R 10.4153/CJM-1996-022-9
%F 10_4153_CJM_1996_022_9

[BG] Babich, V.M. and Grigoreva, N.S., , Funktsional Anal, i Prilozhen. (1) 8 (1974), 71–74. Google Scholar

[BaLR] Bardos, C., Lebeau, G. and Rauch, J., singularities, Invent. Math. 90 (1987), 77–114. Google Scholar

[Be] Besse, A.,Manifolds all of whose geodesies are closed, Springer Verlag, 1978. Google Scholar

[BoS] Boutet de Monvel, L. and Sjostrand, J., Sur la singularity des noyaux de Bergman et de Szego, Asterisque 34-35 (1976), 12S-164. Google Scholar

[FZ] Filippov, V.B. and Zayev, A.B., Rigorous justification of the asymptotic solutions of sliding wave type, J. Soviet Math. (2) 30 (1985), 2395–2406. Google Scholar

[HaL] Hargé, T. and Lebeau, G., Diffraction par un convexe, Invent. Math. (1) 118 (1994), 161–196. Google Scholar

[HS] Helffer, B. and J.Sjöstrand, Résonances en limite semiclassique, Bull. Soc. Math. France (3) 114, Memoire 24/25, (1986). Google Scholar

[L] Lebeau, G., pour la diffraction, Comment. Partial Differential Equations (15) 9 (1984), 1437–1494. Google Scholar

[P] Popov, G., Asymptotics of Green s functions in the shadow, C. R. Acad. Bulgare Sci. (10) 38 (1985), 1287. 1290. Google Scholar

[S1] Sjöstrand, J., Propagation of analytic singularities for second order Dirichlet problems, Comment. Partial Differential Equationa (1) 5 (1980), 41–94. Google Scholar

[S2] Sjöstrand, J., Singularités analytiques microlocales, Astérisque 95 (1982). Google Scholar

[SZ1] Sjostrand, J. and Zworski, M., Estimates on the number of scattering poles near the real axis for strictly convex obstacles, Ann. Inst. Fourier (3) 43(1993), 169-190. Google Scholar

[SZ2] Sjostrand, J., The complex scaling method for scattering by strictly convex obstacles, Institut Mittag-Leffler 10, Ark. Mat., 1992–1993. preprint, to appear. Google Scholar

Cité par Sources :