Poisson relation for the scattering kernel and inverse scattering by obstacles
Séminaire Équations aux dérivées partielles (Polytechnique) (1994-1995), Talk no. 5, 10 p.
@article{SEDP_1994-1995____A5_0,
author = {Stoyanov, L.},
title = {Poisson relation for the scattering kernel and inverse scattering by obstacles},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
year = {1994-1995},
note = {talk:5},
mrnumber = {1362553},
language = {en},
url = {http://www.numdam.org/item/SEDP_1994-1995____A5_0}
}

Stoyanov, L. Poisson relation for the scattering kernel and inverse scattering by obstacles. Séminaire Équations aux dérivées partielles (Polytechnique) (1994-1995), Talk no. 5, 10 p. http://www.numdam.org/item/SEDP_1994-1995____A5_0/

[G] V. Guillemin, Sojourn time and asymptotic properties of the scattering matrix, Publ. RIMS Kyoto Univ. 12 (1977), 69-88. | MR 448453 | Zbl 0381.35064

[GM] V. Guillemin and R. Melrose, The Poisson sumation formula for manifolds with boundary, Adv. in Math. 32 (1979), 204-232. | MR 539531 | Zbl 0421.35082

[H] L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. III, Berlin, Springer, 1985. | Zbl 05129478

[LP1] P. Lax and R. Phillips, Scattering Theory, Academic Press, New York, 1967. | MR 217440 | Zbl 0186.16301

[LP2] P. Lax and R. Phillips, The scattering of sound waves by an obstacle, Comm. Pure Appl. Math. 30 (1977), 195-233. | MR 442510 | Zbl 0335.35075

[Ma] 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

[MaT] A. Majda and M. Taylor, Inverse scattering problems for transparant obstacles, electromagnetic waves and hyperbolic systems, Commun. Partial Diff. Equations 2 (1977), 395-438. | MR 437946 | Zbl 0373.35055

[M1] R. Melrose, Microlocal parametrices for diffractive boundary value problems, Duke Math. J. 42 (1975), 605-635. | MR 517101 | Zbl 0368.35055

[M2] R. Melrose, Equivalence of glancing hypersurfaces, Invent. Math. 37, 165-191 (1976) | MR 436225 | Zbl 0354.53033

[M3] R. Melrose, Geometric Scattering Theory, Lectures at Stanford University, M.I.T. 1994. | MR 1350074 | Zbl 0849.58071

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

[P] V. Petkov, High frequency asymptotics of the scattering amplitude for non-convex bodies. Commun. Partial Diff. Equations 5 (1980), 293-329. | MR 562545 | Zbl 0435.35065

[PS1] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems, John Wiley & Sons, Chichester, 1992. | MR 1172998 | Zbl 0761.35077

[PS2] V. Petkov and L. Stoyanov, Sojourn times of trapping rays and the behaviour of the modified resolvent of the Laplacian, Ann. Inst. Henri Poincare (Physique Theorique), to appear. | Numdam | MR 1313359 | Zbl 0838.35093

[So] H. Soga, Singularities of the scattering kernel for convex obstacles, J. Math. Kyoto Univ. 22 (1983), 729-765. | MR 685528 | Zbl 0511.35070

[St1] L. Stoyanov, Regularity properties of the generalized Hamiltonian flow, Seminaire EDP, Ecole Polytechnique, Exposé, 1992 -1993. | Numdam | MR 1240547 | Zbl 0881.58028

[St2] L. Stoyanov, Generalized Hamiltonian flow and Poisson relation for the scattering kernel, Preprint, Maths. Dept., University of Western Australia 1994.

[T] M. Taylor, Grazing rays and reflection of singularities to wave equations, Commun. Pure Appl. Math. 29 (1978), 1-38. | MR 397175 | Zbl 0318.35009

[Y] K. Yamamoto, Characterization of a convex obstacle by singularities of the scattering kernel, J. Diff. Equations 64 (1986), 283-293. | MR 857711 | Zbl 0611.35066