Le comportement de la résolvante modifiée du laplacien pour des obstacles captifs

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1. [BGR] C. Bardos, J.C. Guillot, J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non-borné. Applications à la théorie de diffusion, Comm. PDE, 7 (1982), 905-958. Zbl0496.35067MR668585
2. [CPS] F. Cardoso, V. Petkov, L. Stoyanov, Singularities of the scattering kernel for generic obstacles, Ann. Inst. H. Poincaré (Physique théorique), 53 (1990), 445-466. Zbl0729.35099MR1096103
3. [G] C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes, Bulletin de S.M.F., Mémoire n° 31, 116 (1988). Zbl0654.35081MR998698
4. [H] L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. III, Pseudo-differential operators, Berlin; Springer, 1985. Zbl1115.35005
5. [I1] M. Ikawa, Precise information on the poles of the scattering matrix for two strictly convex obstacles. J. Math. Kyoto Univ., 27 (1987), 69-102. Zbl0637.35068MR878491
6. [I2] M. Ikawa, Decay of solutions of the wave equation in the exterior of several strictly convex bodies, Ann. Inst. Fourier, 38 (1988), 113-146. Zbl0636.35045MR949013
7. [I3] M. Ikawa, On the existence of the poles of the scattering matrix for several convex bodies, Proc. Japan Acad., 64, Ser. A (1988), 91-93. Zbl0704.35113MR966394
8. [LP] P. Lax and R. Phillips, Scattering Theory, New-York, Academic Press, 1967. Zbl0186.16301MR217440
9. [MS] R. Melrose, J. Sjöstrand, Singularities in boundary value problems, I, Comm. Pure Appl. Math., 31 (1978), 593-617, II, 35 (1982), 129-168. Zbl0546.35083
10. [P1] V. Petkov, High frequency asymptotics of the scattering amplitude for non-convex bodies. Comm. PDE, 5 (1980), 293-329. Zbl0435.35065MR562545
11. [P2] V. Petkov, Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes, Séminaire EDP, Exposé VIII, Ecole Polytechnique, 1989-1990. Zbl0707.35092MR1073183
12. [P3] V. Petkov, The behaviour of the modified resolvent of the Laplacian in the exterior of several convex obstacles, Preprint 1992. 
13. [PS1] V. Petkov, L. Stoyanov, Periods of multiple reflecting geodesics and inverse spectral results, Amer. J. Math., 109 (1987), 619-668. Zbl0652.35027MR900034
14. [PS2] V. Petkov, L. Stoyanov, Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles, Trans. Amer. Math. Soc., 312 (1989), 203-235. Zbl0685.35083MR929661
15. [PS3] V. Petkov, L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems, John Wiley & Sons, Chichester, 1992. Zbl0761.35077MR1172998
16. [R] J. Ralston, Solutions of the wave equation with localized energy, Comm. Pure Appl. Math., 22 (1969), 807-823. Zbl0209.40402MR254433
17. [S1] L. Stoyanov, Nonexistence of generalized scattering rays and singularities of the scattering kernel for generic domains in R3, Proc. Amer. Math. Soc., 113 (1991), 847-856. Zbl0742.58056MR1070532
18. [S2] L. Stoyanov, On the singularities of the scattering kernel, Preprint 1991. 
19. [S3] L. Stoyanov, Continuity properties of the generalized geodesic flow and singularities of the scattering kernel, in preparation. 
20. [V] B. Vainberg, Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach Sci. Publ. Ltd., 1988. Zbl0743.35001MR1054376

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