@article{AIHPA_1995__62_1_17_0, author = {Petkov, Vesselin and Stoyanov, Latchezar}, title = {Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {17--45}, publisher = {Gauthier-Villars}, volume = {62}, number = {1}, year = {1995}, mrnumber = {1313359}, zbl = {0838.35093}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1995__62_1_17_0/} }
TY - JOUR AU - Petkov, Vesselin AU - Stoyanov, Latchezar TI - Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian JO - Annales de l'I.H.P. Physique théorique PY - 1995 SP - 17 EP - 45 VL - 62 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1995__62_1_17_0/ LA - en ID - AIHPA_1995__62_1_17_0 ER -
%0 Journal Article %A Petkov, Vesselin %A Stoyanov, Latchezar %T Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian %J Annales de l'I.H.P. Physique théorique %D 1995 %P 17-45 %V 62 %N 1 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1995__62_1_17_0/ %G en %F AIHPA_1995__62_1_17_0
Petkov, Vesselin; Stoyanov, Latchezar. Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian. Annales de l'I.H.P. Physique théorique, Tome 62 (1995) no. 1, pp. 17-45. http://www.numdam.org/item/AIHPA_1995__62_1_17_0/
[BGR] La relation de Poisson pour l'équation des ondes dans un ouvert non-borné. Comm. PDE, Vol. 7, 1982, pp. 905-958. | MR | Zbl
, and ,[CPS] Singularities of the scattering kernel for generic obstacles. Ann. Inst. Henri Poincaré (Physique théorique), Vol. 53, 1990, pp. 445-466. | Numdam | MR | Zbl
, and ,[G] Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes. Bull. de S.M.F., Vol. 116, Mémoire n° 31, 1988. | Numdam | MR
,[GGu] Stabler Mappings and their Singularities, Berlin, Springer, 1973. | MR | Zbl
and ,[Gu] Sojourn time and asymptotic properties of the scattering matrix. Publ. RIMS Kyoto Univ., Vol. 12, 1977, pp. 69-88. | MR | Zbl
,[HI] The Analysis of Linear Partial Differential Operators, Vol. I. Berlin, Springer, 1985. | MR
,[H2] The Analysis of Linear Partial Differential Operators, Vol. III, Berlin, Springer, 1985. | MR | Zbl
,[11] 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
,[12] Decay of solutions of the wave equation in the exterior of several strictly convex bodies. Ann. Inst. Fourier, Vol. 38, 1988, pp. 113-146. | Numdam | MR | Zbl
,[13] 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
,[14] On scattering by obstacles, Proceedings of ICM-90, Springer-Verlag, 1991, pp. 1145-1154. | MR | Zbl
,[LP] Scattering Theory. New York, Academic Press, 1967. | MR | Zbl
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 | Zbl
,[MS] Singularities in boundary value problems. I, II. Comm. Pure Appl. Math., Vol. 31, 1978, pp. 593-617 and Vol. 37, 1982, pp. 129-168. | MR | Zbl
and ,[P1] Scattering Theory for Hyperbolic Operators. Amsterdam, North-Holland, 1989. | MR | Zbl
,[P2] Le comportement de la résolvante modifiée du Laplacien pour des obstacles captifs. Séminaire EDP, Exposé XVIII, École Polytechnique, 1991-1992. | Numdam | MR | Zbl
,[PS1] Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math., Vol. 109, 1987, pp. 619-668. | MR | Zbl
and ,[PS2] Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc., Vol. 312, 1989, pp. 203-235. | MR | Zbl
and ,[PS3] Geometry of Reflecting Rays and Inverse Spectral Problems. Chichester, John Wiley & Sons, 1992. | Zbl
and ,[SjZ1] Lower bounds on the number of scattering poles. Comm. PDE, Vol. 18, 1993, pp. 847-857. | MR | Zbl
and ,[SjZ2] Lower bounds on the number of scattering poles, II. J. Funct. Anal., Vol. 123, 1994, pp. 336-367. | MR | Zbl
and ,[St] An inverse scattering resultfor several convex bodies. Preprint, Math. Dept., Univ. of Western Australia, 1993.
,[V] Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Sci. Publ. Ltd., 1988. | MR
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