Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian
Petkov, Vesselin ; Stoyanov, Latchezar
Annales de l'I.H.P. Physique théorique, Tome 63 (1995), p. 17-45 / Harvested from Numdam
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@article{AIHPA_1995__62_1_17_0,
     author = {Petkov, Vesselin and Stoyanov, Luchezar N.},
     title = {Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {63},
     year = {1995},
     pages = {17-45},
     mrnumber = {1313359},
     zbl = {0838.35093},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1995__62_1_17_0}
}

Petkov, Vesselin; Stoyanov, Latchezar. Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 17-45. http://gdmltest.u-ga.fr/item/AIHPA_1995__62_1_17_0/

[BGR] C. Bardos, J.C. Gumlot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non-borné. Comm. PDE, Vol. 7, 1982, pp. 905-958. | MR 668585 | Zbl 0496.35067

[CPS] F. Cardoso, V. Petkov and L. Stoyanov, Singularities of the scattering kernel for generic obstacles. Ann. Inst. Henri Poincaré (Physique théorique), Vol. 53, 1990, pp. 445-466. | Numdam | MR 1096103 | Zbl 0729.35099

[G] C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes. Bull. de S.M.F., Vol. 116, Mémoire n° 31, 1988. | Numdam | MR 998698

[GGu] M. Golubitskii and V. Guillemin, Stabler Mappings and their Singularities, Berlin, Springer, 1973. | MR 341518 | Zbl 0294.58004

[Gu] V. Guillemin, Sojourn time and asymptotic properties of the scattering matrix. Publ. RIMS Kyoto Univ., Vol. 12, 1977, pp. 69-88. | MR 448453 | Zbl 0381.35064

[HI] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I. Berlin, Springer, 1985. | MR 404822

[H2] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Berlin, Springer, 1985. | MR 404822 | Zbl 0601.35001

[11] M. Ikawa, Precise information on the poles of the scattering matrix for two strictly convex obstacles. J. Math. Kyoto Univ., Vol. 27, 1987, pp. 69-102. | MR 878491 | Zbl 0637.35068

[12] M. Ikawa, Decay of solutions of the wave equation in the exterior of several strictly convex bodies. Ann. Inst. Fourier, Vol. 38, 1988, pp. 113-146. | Numdam | MR 949013 | Zbl 0636.35045

[13] M. Ikawa, On the existence of the poles of the scattering matrix for several convex bodies. Proc. Japan Acad., Ser. A, Vol. 64, 1988, pp. 91-93. | MR 966394 | Zbl 0704.35113

[14] M. Ikawa, On scattering by obstacles, Proceedings of ICM-90, Springer-Verlag, 1991, pp. 1145-1154. | MR 1159299 | Zbl 0757.35055

[LP] P. Lax and R. Phillips, Scattering Theory. New York, Academic Press, 1967. | MR 217440 | Zbl 0186.16301

[Ma] A. Majda, A representation formula for the scattering operator and the inverse problem for arbitrary bodies. Comm. Pure Appl. Math., Vol. 30, 1977, pp. 165- 194. | MR 435625 | Zbl 0335.35076

[MS] R. Melrose and J. Sjöstrand, Singularities in boundary value problems. I, II. Comm. Pure Appl. Math., Vol. 31, 1978, pp. 593-617 and Vol. 37, 1982, pp. 129-168. | MR 492794 | Zbl 0368.35020

[P1] V. Petkov, Scattering Theory for Hyperbolic Operators. Amsterdam, North-Holland, 1989. | MR 1028780 | Zbl 0687.35067

[P2] V. Petkov, Le comportement de la résolvante modifiée du Laplacien pour des obstacles captifs. Séminaire EDP, Exposé XVIII, École Polytechnique, 1991-1992. | Numdam | MR 1226497 | Zbl 0850.35069

[PS1] V. Petkov and L. Stoyanov, Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math., Vol. 109, 1987, pp. 619-668. | MR 900034 | Zbl 0652.35027

[PS2] V. Petkov and L. Stoyanov, Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc., Vol. 312, 1989, pp. 203-235. | MR 929661 | Zbl 0685.35083

[PS3] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems. Chichester, John Wiley & Sons, 1992. | Zbl 0761.35077

[SjZ1] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles. Comm. PDE, Vol. 18, 1993, pp. 847-857. | MR 1218521 | Zbl 0784.35070

[SjZ2] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, II. J. Funct. Anal., Vol. 123, 1994, pp. 336-367. | MR 1283032 | Zbl 0823.35137

[St] L. Stoyanov, An inverse scattering resultfor several convex bodies. Preprint, Math. Dept., Univ. of Western Australia, 1993.

[V] B. Vainberg, Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Sci. Publ. Ltd., 1988. | MR 1054376