Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian
Vesselin Petkov; Latchezar Stoyanov
Annales de l'I.H.P. Physique théorique (1995)
- Volume: 62, Issue: 1, page 17-45
- ISSN: 0246-0211
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topPetkov, Vesselin, and 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 62.1 (1995): 17-45. <http://eudml.org/doc/76666>.
@article{Petkov1995,
author = {Petkov, Vesselin, Stoyanov, Latchezar},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {scattering rays; singularities of the scattering kernel; scattering matrix; obstacles},
language = {eng},
number = {1},
pages = {17-45},
publisher = {Gauthier-Villars},
title = {Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian},
url = {http://eudml.org/doc/76666},
volume = {62},
year = {1995},
}
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
PB - Gauthier-Villars
VL - 62
IS - 1
SP - 17
EP - 45
LA - eng
KW - scattering rays; singularities of the scattering kernel; scattering matrix; obstacles
UR - http://eudml.org/doc/76666
ER -
References
top- [BGR] C. Bardos, J.C. Gumlot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non-borné. Comm. PDE, Vol. 7, 1982, pp. 905-958. Zbl0496.35067MR668585
- [CPS] F. Cardoso, V. Petkov and L. Stoyanov, Singularities of the scattering kernel for generic obstacles. Ann. Inst. Henri Poincaré (Physique théorique), Vol. 53, 1990, pp. 445-466. Zbl0729.35099MR1096103
- [G] C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes. Bull. de S.M.F., Vol. 116, Mémoire n° 31, 1988. Zbl0654.35081MR998698
- [GGu] M. Golubitskii and V. Guillemin, Stabler Mappings and their Singularities, Berlin, Springer, 1973. Zbl0294.58004MR341518
- [Gu] V. Guillemin, Sojourn time and asymptotic properties of the scattering matrix. Publ. RIMS Kyoto Univ., Vol. 12, 1977, pp. 69-88. Zbl0381.35064MR448453
- [HI] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I. Berlin, Springer, 1985. MR404822
- [H2] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Berlin, Springer, 1985. Zbl0601.35001MR404822
- [11] 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. Zbl0637.35068MR878491
- [12] M. Ikawa, Decay of solutions of the wave equation in the exterior of several strictly convex bodies. Ann. Inst. Fourier, Vol. 38, 1988, pp. 113-146. Zbl0636.35045MR949013
- [13] 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. Zbl0704.35113MR966394
- [14] M. Ikawa, On scattering by obstacles, Proceedings of ICM-90, Springer-Verlag, 1991, pp. 1145-1154. Zbl0757.35055MR1159299
- [LP] P. Lax and R. Phillips, Scattering Theory. New York, Academic Press, 1967. Zbl0186.16301MR217440
- [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. Zbl0335.35076MR435625
- [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. 37, 1982, pp. 129-168. Zbl0368.35020MR492794
- [P1] V. Petkov, Scattering Theory for Hyperbolic Operators. Amsterdam, North–Holland, 1989. Zbl0687.35067MR1028780
- [P2] V. Petkov, Le comportement de la résolvante modifiée du Laplacien pour des obstacles captifs. Séminaire EDP, Exposé XVIII, École Polytechnique, 1991-1992. Zbl0850.35069MR1226497
- [PS1] V. Petkov and L. Stoyanov, Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math., Vol. 109, 1987, pp. 619-668. Zbl0652.35027MR900034
- [PS2] V. Petkov and L. Stoyanov, Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc., Vol. 312, 1989, pp. 203-235. Zbl0685.35083MR929661
- [PS3] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems. Chichester, John Wiley & Sons, 1992. Zbl0761.35077
- [SjZ1] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles. Comm. PDE, Vol. 18, 1993, pp. 847-857. Zbl0784.35070MR1218521
- [SjZ2] 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
- [St] L. Stoyanov, An inverse scattering resultfor several convex bodies. Preprint, Math. Dept., Univ. of Western Australia, 1993.
- [V] B. Vainberg, Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Sci. Publ. Ltd., 1988. Zbl0518.35002MR1054376
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