Singularities of the scattering kernel for trapping obstacles
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 29 (1996) no. 6, pp. 737-756.
@article{ASENS_1996_4_29_6_737_0,
     author = {Petkov, Vesselin and Stoyanov, Latchezar},
     title = {Singularities of the scattering kernel for trapping obstacles},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {737--756},
     publisher = {Elsevier},
     volume = {Ser. 4, 29},
     number = {6},
     year = {1996},
     doi = {10.24033/asens.1752},
     mrnumber = {97k:35187},
     zbl = {0887.35114},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1752/}
}
TY  - JOUR
AU  - Petkov, Vesselin
AU  - Stoyanov, Latchezar
TI  - Singularities of the scattering kernel for trapping obstacles
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1996
SP  - 737
EP  - 756
VL  - 29
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.24033/asens.1752/
DO  - 10.24033/asens.1752
LA  - en
ID  - ASENS_1996_4_29_6_737_0
ER  - 
%0 Journal Article
%A Petkov, Vesselin
%A Stoyanov, Latchezar
%T Singularities of the scattering kernel for trapping obstacles
%J Annales scientifiques de l'École Normale Supérieure
%D 1996
%P 737-756
%V 29
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.24033/asens.1752/
%R 10.24033/asens.1752
%G en
%F ASENS_1996_4_29_6_737_0
Petkov, Vesselin; Stoyanov, Latchezar. Singularities of the scattering kernel for trapping obstacles. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 29 (1996) no. 6, pp. 737-756. doi : 10.24033/asens.1752. http://www.numdam.org/articles/10.24033/asens.1752/

[BGR] C. Bardos, J. C. Guillot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non-borné (Commun. Partial Diff. Equations, Vol. 7, 1982, pp. 905-958). | MR | Zbl

[BLR] C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient condition for the observation, control and stabilization of waves from the boundary (SIAM J. Control and Optimization, Vol. 30, 1992, pp. 1024-1065). | MR | Zbl

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

[Fa1] L. Farhy, Distribution near real axis of the scattering poles generated by a non-periodic ray (Ann. Inst. H. Poincaré (Physique théorique), Vol. 60, 1994, pp. 291-302). | Numdam | MR | Zbl

[Fa2] L. Farhy, Lower bounds on the number of scattering poles under lines parallel to real axis (Commun. Partial Diff. Equations, Vol. 20, 1995, pp. 729-740). | MR | Zbl

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

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

[H] L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. III. Berlin, Springer 1985. | Zbl

[I1] 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 | Zbl

[I2] 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 | Zbl

[I3] M. Ikawa, On scattering by obstacles, Proceedings ICM-90, Springer-Verlag, Berlin, 1991, pp. 1145-1154. | MR | Zbl

[LP1] P. Lax and R. Phillips, Scattering Theory, New York, Academic Press, 1967. | Zbl

[LP2] P. Lax and R. Phillips, Scattering theory for the acoustical equation in an even number of space dimensions (Indiana Univ. Math. J., Vol. 22, 1972, pp. 101-134). | MR | Zbl

[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 | Zbl

[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. 35, 1982, pp. 129-168). | Zbl

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

[PS1] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems, Chichester, John Wiley & Sons, 1992. | MR | Zbl

[PS2] V. Petkov and L. Stoyanov, Sojourn times of trapping rays and the behaviour of the modified resolvent of the Laplacian (Ann. Inst. H. Poincaré (Physique théorique), Vol. 62, 1995, pp. 17-45). | Numdam | MR | Zbl

[Ra] J. Ralston, Solutions of the wave equation with localized energy (Comm. Pure Appl. Math., Vol. 22, 1969, pp. 807-823). | MR | Zbl

[So] H. Soga, Singularities of the scattering kernel for convex obstacles (J. Math. Kyoto Univ., Vol. 22, 1983, pp. 729-765). | MR | Zbl

[SjZ] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles (Commun. Partial Diff. Equations, Vol. 18, 1993, pp. 847-857). | MR | Zbl

[St1] L. Stoyanov, Generalized Hamiltonian flow and Poisson relation for the scattering kernel (Maths. Department, Univ. of Western Australia, Research Report 10, 1994).

[St2] L. Stoyanov, Poisson relation for the scattering kernel and inverse scattering by obstacles (Séminaire EDP, Exposé V, Ecole Polytechnique, 1994-1995). | Numdam | Zbl

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

[Vo1] G. Vodev, Sharp bound on the number of scattering poles in even-dimensional spaces (Duke Math. J., Vol. 74, 1994, pp. 1-17). | MR | Zbl

[Vo2] G. Vodev, Sharp bounds on the number of scattering poles in the two dimensional case (Math. Nachr., Vol. 170, 1994, pp. 287-297). | MR | Zbl

Cité par Sources :