Estimates for the cut-off resolvent of the Laplacian for trapping obstacles

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1. J.-F. Bony, Résonances dans des domaines de taille h, Inter. Math. Res. Notes, 16 (2001), 817-847. Zbl1034.35084MR1853138
2. J.-F. Bony and L. Michel, Microlocalization of resonant states and estimates of the residue of the scattering amplitude Comm. Math. Phys. 246 (2004), no. 2, 375–402. Zbl1062.35053MR2048563
3. J.-F. Bony and V. Petkov, Resonances for non-trapping time-periodic perturbations, J. Phys. A: Math. Gen. 37 (2004), 9439-9449. Zbl1137.35399MR2095429
4. J.-F. Bony and V. Petkov, Resolvent estimates and local energy decay of hyperbolic equations, Around Hyberbolic Systems, Conference to the memory of Stefano Benvenutti, Ferrara 2005, to appear. MR2273096
5. N. Burq, Décroissance de l’énergie locale de l’équation des ondes pour le problème extérieur et absence de résonances au voisinage du réel, Acta Math. 180 (1998), 1-29. Zbl0918.35081
6. N. Burq, Semi-classical estimates for the resolvent in non-trapping geometries, Inter. Math. Res. Notes, 5 (2002), 221-241. Zbl1161.81368MR1876933
7. N. Burq, Global Strichartz estimates for nontrapping geometries: About an article by H. Smith and C. Sogge, Comm. Partial Differential Equations, 28 (2003), no. 9-10, 1675–1683. Zbl1026.35020MR2001179
8. N. Burq, Smoothing effect for Schrödinger boundary value problems, Duke Math. J. 123 (2004), no. 2, 403–427. Zbl1061.35024MR2066943
9. M. Ikawa, Decay of solutions of the wave equation in the exterior of several convex bodies, Ann. Inst. Fourier, 38 (1989), 113-146. Zbl0636.35045MR949013
10. C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes, Bulletin de SMF, Mémoire no. 31, 116(1), (1988). Zbl0654.35081MR998698
11. I. Herbst, Contraction semigroups and the spectrum of $A_1\otimes I+I\otimes A_2$, J. Oper. Theory, 7 (1982), 61-78. Zbl0484.47017MR650193
12. R. Melrose and J. Sjöstrand, Singularities of boundary value problems, Comm. Pure Appl. Math. I, 31 (1978), 593-617, II, 35 (1982), 129-168. Zbl0546.35083
13. C. Morawetz, Decay estimates of the exterior problem for the wave equation, Comm. Appl. Math. 28 (1975), 229-264. Zbl0304.35064MR372432
14. P. D. Lax and R.S. Phillips, Scattering Theory, Academic Press, 2nd Edition, 1989. Zbl0697.35004MR1037774
15. V. Petkov and L. Stoyanov, Trapping obstacles and singularities of the scattering kernel, Colloque Franco-Tunisien d’EDP, Hammamet, 2003, Séminaires et Congrès, SMF, to appear. Zbl0887.35114
16. V. Petkov, Global Strichartz estimates for the wave equation with time-periodic potentials, J. Funct. Anal., to appear. Zbl1092.35018MR2225457
17. G. Popov and G. Vodev, Distribution of the resonances and local energy decay in the transmission problem, Asymptotic Analysis, 19 (1999), 253-265. Zbl0931.35115MR1696217
18. J. Ralston, Solutions of the wave equation with localized energy, Comm. Pure Appl. Math. 22 (1969), 807–823. Zbl0209.40402MR254433
19. J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4 (1991), 729-769. Zbl0752.35046MR1115789
20. J. Sjöstrand, A trace formula and review of some estimates for resonances, Microlocal Analysis and spectral theory, NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci. 490 (1997), 377-437. Zbl0877.35090MR1451399
21. J. Sjöstrand, Resonances for bottles and related trace formulae, Math. Nachr. 221 (2001), 95-149. Zbl0979.35109MR1806367
22. S. H. Tang and M. Zworski, Resonances expansions of scattered waves, Comm. Pure Appl. Math. 53 (2000), 1305-1334. Zbl1032.35148MR1768812
23. G. Vodev, On the uniform decay of the local energy, Serdica Math. J. 25 (1999), 191–206. Zbl0937.35118MR1742776