Scattering poles for connected sums of euclidean space and Zoll manifolds
Annales de l'I.H.P. Physique théorique, Tome 65 (1996) no. 2, pp. 163-174.
@article{AIHPA_1996__65_2_163_0,
     author = {Farhy, L. S. and Tsanov, V. V.},
     title = {Scattering poles for connected sums of euclidean space and {Zoll} manifolds},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {163--174},
     publisher = {Gauthier-Villars},
     volume = {65},
     number = {2},
     year = {1996},
     mrnumber = {1411265},
     zbl = {0915.58107},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1996__65_2_163_0/}
}
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Farhy, L. S.; Tsanov, V. V. Scattering poles for connected sums of euclidean space and Zoll manifolds. Annales de l'I.H.P. Physique théorique, Tome 65 (1996) no. 2, pp. 163-174. http://www.numdam.org/item/AIHPA_1996__65_2_163_0/

[1] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété Riemannienne, Lecture Notes in Math., Vol. 194, Berlin, 1971. | Zbl

[2] A.L. Besse, Manifolds all of whose geodesics are closed, Springer-Verlag, 1978. | MR | Zbl

[3] J. Duistermaat and V. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math., Vol. 29, 1975, pp. 39-79. | MR | Zbl

[4] L.S. Farhy, Distribution near the real axis of scattering poles generated by a non-hyperbolic periodic ray, Ann. Inst. H. Poincaré, Vol. 60, 1994, pp. 291-302. | Numdam | MR | Zbl

[5] L.S. Farhy, Lower bounds on the number of scattering poles under lines parallel to the real axis, Comm. P.D.E., Vol. 20, 1995, pp. 729-740. | MR | Zbl

[6] L.S. Farhy, Trapping obstacles with non-hyperbolic periodic ray, asymptotic behaviour of solutions, Math. Z., Vol. 217, 1994, pp. 143-165. | MR | Zbl

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

[8] L. Guillopé, Majorations à la Weyl pour le nombre de résonances à une perturbation compacte du laplacien euclidien, preprint.

[9] L. Hörmander, The analysis of linear partial differential operators, Springer-Verlag, 1983-1985.

[10] M. Ikawa, On the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ., Vol. 23, 1983, pp. 127-194. | MR | Zbl

[11] M. Ikawa, Trapping obstacles with a sequence of poles of the scattering matrix converging to the real axis, Osaka J. Math., Vol. 22, 1985, pp. 657-689. | MR | Zbl

[12] P. Lax and R.S. Phillips, Scattering theory, Academic Press, New York, 1967. | MR | Zbl

[13] P. Lax and R.S. Phillips, Decaying modes for the wave equation in the exterior of an obstacle, Comm. Pure Appl. Math., Vol. 22, 1969, pp. 737-787. | MR | Zbl

[14] R.B. Melrose, Scattering theory and the trace of the wave group, J. of Funct. Anal., Vol. 45, 1982, pp. 29-40. | MR | Zbl

[15] R.B. Melrose, Polynomial bounds on the number of scattering poles, J. of Funct. Anal., Vol. 53, 1983, pp. 287-303. | MR | Zbl

[16] V. Petkov and G. Vodev, Upper bounds on the number of scattering poles and the Lax-Phillips conjecture, Asympt. Analysis, Vol. 7, 1993, pp. 97-104. | MR | Zbl

[17] J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. of Amer. Math. Soc., Vol. 4, 1991, pp. 729-769. | MR | Zbl

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

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

[20] G. Vodev, Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in Rn, Math. Ann., Vol. 291, 1991, pp. 39-49. | MR | Zbl

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

[22] A. Weinstein, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J., Vol. 44, 1977, pp. 883-892. | MR | Zbl

[23] M. Zworski, Counting scattering poles, Spectral and Scattering Theory, M. Ikawa ed., Marcel Dekker, 1995, pp. 301-331. | MR | Zbl