Stoyanov, Luchezar
Generalized Hamilton flow and Poisson relation for the scattering kernel
Annales scientifiques de l'École Normale Supérieure, Série 4 : Tome 33 (2000) no. 3 , p. 361-382
Zbl 0963.37055 | MR 2001g:37120
doi : 10.1016/s0012-9593(00)00115-4
URL stable : http://www.numdam.org/item?id=ASENS_2000_4_33_3_361_0

Bibliographie

[1] Abraham R., Marsden J., Foundations of Mechanics, London, Benjamin/Cummings, 1978. MR 81e:58025 | Zbl 0393.70001

[2] Edgar G., Measure, Topology, and Fractal Geometry, New York, Springer, 1990. MR 92a:54001 | Zbl 0727.28003

[3] Guillemin G., Sojourn time and asymptotic properties of the scattering matrix, Publ. RIMS Kyoto Univ. 12 (1977) 69-88. MR 56 #6759 | Zbl 0381.35064

[4] Hörmander L., The Analysis of Linear Partial Differential Operators, Vol. III, Berlin, Springer, 1985. Zbl 0601.35001

[5] Lax P., Phillips R., Scattering Theory, Academic Press, New York, 1967. Zbl 0186.16301

[6] Melrose R., Microlocal parametrices for diffractive boundary value problems, Duke Math. J. 42 (1975) 605-635. MR 58 #24409 | Zbl 0368.35055

[7] Melrose R., Geometric Scattering Theory, Cambridge Univ. Press, Cambridge, 1994. Zbl 0849.58071

[8] Melrose R., Sjöstrand J., Singularities in boundary value problems, I, Comm. Pure Appl. Math. 31 (1978) 593-617. Zbl 0368.35020

[9] Melrose R., Sjöstrand J., Singularities in boundary value problems, II, Comm. Pure Appl. Math. 35 (1982) 129-168. Zbl 0546.35083

[10] Morawetz C., Ralston J., Strauss W., Decay of solutions to the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math. 30 (1977) 447-508. MR 58 #23091a | Zbl 0372.35008

[11] Petkov V., High frequency asymptotics of the scattering amplitude for non-convex bodies, Comm. Partial Differential Equations 5 (1980) 293-329. MR 82c:35061 | Zbl 0435.35065

[12] Petkov V., Stoyanov L., Geometry of Reflecting Rays and Inverse Spectral Problems, Chichester, Wiley, 1992. MR 93i:58161 | Zbl 0761.35077

[13] Petkov V., Stoyanov L., Sojourn times of trapping rays and the behaviour of the modified resolvent of the Laplacian, Ann. Inst. Henri Poincaré (Physique Théorique) 62 (1995) 17-45. Numdam | MR 96g:58199 | Zbl 0838.35093

[14] Stoyanov L., Rigidity of the scattering length spectrum, Preprint 1997/1998.

[15] Stoyanov L., Poisson relation for the scattering kernel and inverse scattering by obstacles, in : Séminaire EDP, Exposé V, École Polytechnique, 1994-1995. Numdam | Zbl 0888.58070

[16] Taylor M., Grazing rays and reflection of singularities to wave equations, Comm. Pure Appl. Math. 29 (1976) 1-38. MR 53 #1035 | Zbl 0318.35009