Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes
Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990), Talk no. 8, 12 p.
@article{SEDP_1989-1990____A10_0,
     author = {Petkov, V. M.},
     title = {Les singularit\'es du noyau de l'op\'erateur de diffusion pour des obstacles non-convexes},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1989-1990},
     note = {talk:8},
     zbl = {0707.35092},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_1989-1990____A10_0}
}
Petkov, V. M. Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes. Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990), Talk no. 8, 12 p. http://www.numdam.org/item/SEDP_1989-1990____A10_0/

[1] K. Andersson and R. Melrose: The propagation of singularities along gliding rays. Invent. Math., 41 (1977), 197-232. | MR 494322 | Zbl 0373.35053

[2] F. Cardoso, V. Petkov and L. Stojanov: Singularities of the scattering kernel for generic obstacles. Preprint. | Numdam | Zbl 0729.35099

[3] M. Golubitsky and V. Guillemin: Stable Mappings and Their Singularities. Springer Verlag, New York, 1973. | MR 341518 | Zbl 0294.58004

[4] V. Guillemin: Sojourn time and asymptotic properties of the scattering matrix. Publ. Res. Inst. Math. Sci., Supl. 12 (1977), 69-88. | MR 448453 | Zbl 0381.35064

[5] P. Lax and R. Phillips: Scattering Theory. Academic Press, New York, 1967. | MR 217440 | Zbl 0186.16301

[6] A. Majda: A representation formula for the scattering operator and the inverse problem for arbitrary bodies. Comm. Pure Appl. Math. 30 (1977), 165-194. | MR 435625 | Zbl 0335.35076

[7] R. Melrose: Singularities and energy decay of acoustical scattering. Duke Math. J., 46 (1979), 43-59. | MR 523601 | Zbl 0415.35050

[8] R. Melrose and J. Sjöstrand: Singularities on boundary value problems, I, II. Comm. Pure Appl. Math., 31 (1978), 593-617 and 35 (1982), 129-168. | MR 492794 | Zbl 0546.35083

[9] S. Nakamura: Singularities of the scattering kernel for two convex obstacles. Publ. RIMS Kyoto University, 25 (1989), 223-238. | MR 1003786 | Zbl 0699.35202

[10] S. Nakamura and H. Soga: Singularities of the scattering kernel for two balls. J. Math. Soc. Japan, 40 (1988), 205-220. | MR 930597 | Zbl 0638.35068

[11] V. Petkov: High frequency asymptotics of the scattering amplitude for non-convex bodies. Comm. PDE, 5 (1980), 293-329. | MR 562545 | Zbl 0435.35065

[12] V. Petkov: Scattering Theory for Hyperbolic Operators. North-Holland, Amsterdamn, 1989. | MR 1028780 | Zbl 0687.35067

[13] V. Petkov and L. Stojanov: Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math., 109 (1987), 619-668. | MR 900034 | Zbl 0652.35027

[14] V. Petkov and L. Stojanov: Spectrum of the Poincaré map for periodic reflecting rays in generic domains, Math. Z., 194 (1987), 505-518. | MR 881708 | Zbl 0673.58035

[15] V. Petkov and L. Stojanov: On the number of periodic rays in generic domains. Ergodic Theory and Dynamical Systems, 8 (1988), 81-91. | MR 939062 | Zbl 0668.58005

[16] V. Petkov and L. Stojanov: Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc. 312 (1989), 203-235. | MR 929661 | Zbl 0685.35083

[17] V. Petkov and L. Stojanov: Singularities of the scattering kernel for a class of starshaped non-convex obstacles. Math. Appl. Comput., (to appear). | Zbl 0705.35095

[18] H. Soga: Conditions against rapid decrease of oscillatory integrals and their applications to inverse scattering problems. Osana J. Math., 23 (1986), 441-456. | MR 856897 | Zbl 0617.35104

[19] L. Stojanov: Unpublished manuscript, 1989.

[20] L. Stojanov: Nonexistence of generalized scattering rays and singularities of the scattering kernel for generic domains in R3. Preprint, 1989. | Zbl 0742.58056

[21] B. Vainberg: Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Sci. Publ., 1988. | MR 1054376 | Zbl 0743.35001