@article{ASENS_1996_4_29_6_737_0, author = {Petkov, Vesselin and Stoyanov, Luchezar N.}, title = {Singularities of the scattering kernel for trapping obstacles}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {29}, year = {1996}, pages = {737-756}, doi = {10.24033/asens.1752}, mrnumber = {97k:35187}, zbl = {0887.35114}, language = {en}, url = {http://dml.mathdoc.fr/item/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, Tome 29 (1996) pp. 737-756. doi : 10.24033/asens.1752. http://gdmltest.u-ga.fr/item/ASENS_1996_4_29_6_737_0/
[BGR] 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 84d:35120 | Zbl 0496.35067
, and ,[BLR] 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 94b:93067 | Zbl 0786.93009
, and ,[CPS] Singularities of the scattering kernel for generic obstacles (Ann. Inst. H. Poincaré (Physique théorique), Vol. 53, 1990, pp. 445-466). | Numdam | MR 92i:35073 | Zbl 0729.35099
, and ,[Fa1] 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 95h:35165 | Zbl 0808.35091
,[Fa2] 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 96a:35140 | Zbl 0822.35105
,[G] 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 91e:35168 | Zbl 0654.35081
,[Gu] Sojourn time and asymptotic properties of the scattering matrix (Publ. RIMS Kyoto Univ., Vol. 12, 1977, pp. 69-88). | MR 56 #6759 | Zbl 0381.35064
,[H] The Analysis of Linear Partial Differential Operators, vol. III. Berlin, Springer 1985. | Zbl 0601.35001
,[I1] 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 88e:35143 | Zbl 0637.35068
,[I2] 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 90i:35211 | Zbl 0704.35113
,[I3] On scattering by obstacles, Proceedings ICM-90, Springer-Verlag, Berlin, 1991, pp. 1145-1154. | MR 1159299 | Zbl 0757.35055
,[LP1] Scattering Theory, New York, Academic Press, 1967. | Zbl 0186.16301
and ,[LP2] Scattering theory for the acoustical equation in an even number of space dimensions (Indiana Univ. Math. J., Vol. 22, 1972, pp. 101-134). | MR 46 #4014 | Zbl 0236.35036
and ,[Ma] 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 55 #8583 | Zbl 0335.35076
,[MS] 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 0368.35020
and ,[P] Scattering Theory for Hyperbolic Operators, Amsterdam, North-Holland, 1989. | MR 91e:35170 | Zbl 0687.35067
,[PS1] Geometry of Reflecting Rays and Inverse Spectral Problems, Chichester, John Wiley & Sons, 1992. | MR 93i:58161 | Zbl 0761.35077
and ,[PS2] 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 96g:58199 | Zbl 0838.35093
and ,[Ra] Solutions of the wave equation with localized energy (Comm. Pure Appl. Math., Vol. 22, 1969, pp. 807-823). | MR 40 #7642 | Zbl 0209.40402
,[So] Singularities of the scattering kernel for convex obstacles (J. Math. Kyoto Univ., Vol. 22, 1983, pp. 729-765). | MR 84c:35085 | Zbl 0511.35070
,[SjZ] Lower bounds on the number of scattering poles (Commun. Partial Diff. Equations, Vol. 18, 1993, pp. 847-857). | MR 94h:35198 | Zbl 0784.35070
and ,[St1] Generalized Hamiltonian flow and Poisson relation for the scattering kernel (Maths. Department, Univ. of Western Australia, Research Report 10, 1994).
,[St2] Poisson relation for the scattering kernel and inverse scattering by obstacles (Séminaire EDP, Exposé V, Ecole Polytechnique, 1994-1995). | Numdam | Zbl 0888.58070
,[V] Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach Sci. Publ. Ltd., 1988. | Zbl 0743.35001
,[Vo1] Sharp bound on the number of scattering poles in even-dimensional spaces (Duke Math. J., Vol. 74, 1994, pp. 1-17). | MR 95e:35153 | Zbl 0813.35075
,[Vo2] Sharp bounds on the number of scattering poles in the two dimensional case (Math. Nachr., Vol. 170, 1994, pp. 287-297). | MR 95i:35209 | Zbl 0829.35091
,