Propagation of singularities in many-body scattering
Vasy, András1
1 Massachusetts Institute of Technology, Department of Mathematics, Cambridge MA (USA)
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 3, pp. 313-402.
DOI : 10.1016/s0012-9593(01)01066-7
Vasy, András 1

1 Massachusetts Institute of Technology, Department of Mathematics, Cambridge MA (USA) 
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Vasy, András. Propagation of singularities in many-body scattering. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 3, pp. 313-402. doi : 10.1016/s0012-9593(01)01066-7. http://archive.numdam.org/articles/10.1016/s0012-9593(01)01066-7/

[1] Bommier A., Propriétés de la matrice de diffusion, Ann. Inst. Henri Poincaré 59 (1993) 237-267. | Numdam | MR | Zbl

[2] Dereziński J., Asymptotic completeness of long-range N-body quantum systems, Ann. Math. 138 (1993) 427-476. | MR | Zbl

[3] Dereziński J., Gérard C., Scattering Theory of Classical Quantum N-particle Systems, Springer, 1997. | MR | Zbl

[4] Froese R.G., Herbst I., Exponential bounds, Comm. Math. Phys. 87 (1982) 429-447. | MR | Zbl

[5] Froese R.G., Herbst I., A new proof of the Mourre estimate, Duke Math. J. 49 (1982) 1075-1085. | MR | Zbl

[6] Gérard C., Isozaki H., Skibsted E., Commutator algebra resolvent estimates, in: Advanced Studies in Pure Mathematics, Vol. 23, 1994, pp. 69-82. | MR

[7] Gérard C., Isozaki H., Skibsted E., N-body resolvent estimates, J. Math. Soc. Japan 48 (1996) 135-160. | MR | Zbl

[8] Graf G.M., Asymptotic completeness for N-body short range systems, Comm. Math. Phys. 132 (1990) 73-101. | MR | Zbl

[9] Hassell A., Vasy A., Symbolic functional calculus, J. Funct. Anal. 173 (2000) 257-283. | MR | Zbl

[10] Helffer B., Sjöstrand J., Équation de Schrödinger avec champ magnétique et équation de Harper. | Zbl

[11] Hörmander L., Fourier integral operators, Acta Mathematica 127 (1971) 79-183. | MR | Zbl

[12] Hörmander L., The Analysis of Linear Partial Differential Operators, Vols. 1-4, Springer-Verlag, 1983.

[13] Ikawa M. (Ed.), Spectral and Scattering Theory, Marcel Dekker, 1994. | MR | Zbl

[14] Isozaki H., Structures of S-matrices for three body Schrödinger operators, Comm. Math. Phys. 146 (1992) 241-258. | MR | Zbl

[15] Isozaki H., A generalization of the radiation condition of Sommerfeld for N-body Schrödinger operators, Duke Math. J. 74 (1994) 557-584. | MR | Zbl

[16] Isozaki H., A uniqueness theorem for the N-body Schrödinger equation and its applications, in: Ikawa M. (Ed.), Spectrial and Scattering Theory, Marcel Dekker, 1994. | MR | Zbl

[17] Jensen A., Propagation estimates for Schrödinger-type operators, Trans. Amer. Math. Soc. 291 (1) (1985) 129-144. | MR | Zbl

[18] Lebeau G., Propagation des ondes dans les variétés à coins, Ann. Scient. Éc. Norm. Sup. 30 (1997) 429-497. | Numdam | MR | Zbl

[19] Mazzeo R., Melrose R.B., Pseudodifferential operators on manifolds with fibred boundaries, Asian J. Math. 2 (1998). | MR | Zbl

[20] Melrose R.B., Differential analysis on manifolds with corners, In preparation.

[21] Melrose R.B., Calculus of conormal distributions on manifolds with corners, Internat. Math. Res. Notices 3 (1992) 51-61. | MR | Zbl

[22] Melrose R.B., Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces, in: Ikawa M. (Ed.), Spectrial and Scattering Theory, Marcel Dekker, 1994. | MR | Zbl

[23] Melrose R.B., Sjöstrand J., Singularities of boundary value problems. I, Comm. Pure Appl. Math. 31 (1978) 593-617. | MR | Zbl

[24] Melrose R.B., Sjöstrand J., Singularities of boundary value problems. II, Comm. Pure Appl. Math. 35 (1982) 129-168. | MR | Zbl

[25] Melrose R.B., Zworski M., Scattering metrics, Inventiones Math. 124 (1996) 389-436. | MR | Zbl

[26] Mourre E., Absence of singular continuous spectrum of certain self-adjoint operators, Comm. Math. Phys. 78 (1981) 391-408. | MR | Zbl

[27] Perry P., Sigal I.M., Simon B., Spectral analysis of N-body Schrödinger operators, Ann. Math. 114 (1981) 519-567. | MR | Zbl

[28] Sigal I.M., Soffer A., N-particle scattering problem, Ann. Math. 125 (1987) 35-108. | MR | Zbl

[29] Sigal I.M., Soffer A., Long-range many-body scattering, Inventiones Math. 99 (1990) 115-143. | MR | Zbl

[30] Sigal I.M., Soffer A., Asymptotic completeness of N≤4-particle systems with the Coulomb-type interactions, Duke Math. J. 71 (1993) 243-298. | Zbl

[31] Sigal I.M., Soffer A., Asymptotic completeness of N-particle long-range scattering, J. Amer. Math. Soc. 7 (1994) 307-334. | MR | Zbl

[32] Sjöstrand J., Propagation of analytic singularities for second order Dirichlet problems, Comm. PDE 5 (1980) 41-94. | MR | Zbl

[33] Skibsted E., Smoothness of N-body scattering amplitudes, Rev. Math. Phys. 4 (1992) 619-658. | MR | Zbl

[34] Taylor M., Grazing rays, Comm. Pure Appl. Math. 29 (1976) 1-38. | MR | Zbl

[35] Vasy A., Asymptotic behavior of generalized eigenfunctions in N-body scattering, J. Funct. Anal. 148 (1997) 170-184. | MR | Zbl

[36] Vasy A., Propagation of singularities in three-body scattering, Ph.D. Thesis, Massachusetts Institute of Technology, 1997.

[37] Vasy A., Structure of the resolvent for three-body potentials, Duke Math. J. 90 (1997) 379-434. | MR | Zbl

[38] Vasy A., Geometric scattering theory for long-range potentials, Int. Math. Res. Notices 1998 (1998) 285-315. | MR | Zbl

[39] Vasy A., Scattering matrices in many-body scattering, Comm. Math. Phys. 200 (1999) 105-124. | MR | Zbl

[40] Vasy A., Propagation of singularities in three-body scattering, Astérisque 262 (2000). | Numdam | MR | Zbl

[41] Wang X.P., Microlocal estimates for N-body Schrödinger operators, J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 40 (1993) 337-385. | MR | Zbl

[42] Yafaev D., Radiation conditions, Comm. Math. Phys. 154 (1993) 523-554. | MR | Zbl

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