Scattering poles for connected sums of euclidean space and Zoll manifolds
Annales de l'I.H.P. Physique théorique (1996)
- Volume: 65, Issue: 2, page 163-174
- ISSN: 0246-0211
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top- [1] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété Riemannienne, Lecture Notes in Math., Vol. 194, Berlin, 1971. Zbl0223.53034
- [2] A.L. Besse, Manifolds all of whose geodesics are closed, Springer-Verlag, 1978. Zbl0387.53010MR496885
- [3] J. Duistermaat and V. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math., Vol. 29, 1975, pp. 39-79. Zbl0307.35071MR405514
- [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. Zbl0808.35091MR1281648
- [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. Zbl0822.35105MR1326904
- [6] L.S. Farhy, Trapping obstacles with non-hyperbolic periodic ray, asymptotic behaviour of solutions, Math. Z., Vol. 217, 1994, pp. 143-165. Zbl0808.35067MR1292178
- [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. Zbl0654.35081MR998698
- [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. Zbl0521.35002
- [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. Zbl0561.35060MR692733
- [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. Zbl0617.35102MR815439
- [12] P. Lax and R.S. Phillips, Scattering theory, Academic Press, New York, 1967. Zbl0186.16301MR1037774
- [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. Zbl0181.38201MR254432
- [14] R.B. Melrose, Scattering theory and the trace of the wave group, J. of Funct. Anal., Vol. 45, 1982, pp. 29-40. Zbl0525.47007MR645644
- [15] R.B. Melrose, Polynomial bounds on the number of scattering poles, J. of Funct. Anal., Vol. 53, 1983, pp. 287-303. Zbl0535.35067MR724031
- [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. Zbl0801.35099MR1225440
- [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. Zbl0752.35046MR1115789
- [18] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, Comm. P.D.E., Vol. 18, 1993, pp. 847-857. Zbl0784.35070MR1218521
- [19] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles II, J. Funct. Anal., Vol. 123, 1994, pp. 336-367. Zbl0823.35137MR1283032
- [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. Zbl0754.35105MR1125006
- [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. Zbl0766.35032MR1163673
- [22] A. Weinstein, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J., Vol. 44, 1977, pp. 883-892. Zbl0385.58013MR482878
- [23] M. Zworski, Counting scattering poles, Spectral and Scattering Theory, M. Ikawa ed., Marcel Dekker, 1995, pp. 301-331. Zbl0823.35139MR1291649