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
Access Full Article
topHow to cite
topFarhy, L. S., and Tsanov, V. V.. "Scattering poles for connected sums of euclidean space and Zoll manifolds." Annales de l'I.H.P. Physique théorique 65.2 (1996): 163-174. <http://eudml.org/doc/76739>.
@article{Farhy1996,
author = {Farhy, L. S., Tsanov, V. V.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {scattering poles; number of resonances; Euclidean space; Zoll manifold},
language = {eng},
number = {2},
pages = {163-174},
publisher = {Gauthier-Villars},
title = {Scattering poles for connected sums of euclidean space and Zoll manifolds},
url = {http://eudml.org/doc/76739},
volume = {65},
year = {1996},
}
TY - JOUR
AU - Farhy, L. S.
AU - Tsanov, V. V.
TI - Scattering poles for connected sums of euclidean space and Zoll manifolds
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 65
IS - 2
SP - 163
EP - 174
LA - eng
KW - scattering poles; number of resonances; Euclidean space; Zoll manifold
UR - http://eudml.org/doc/76739
ER -
References
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
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.