Propagation of singularities in three-body scattering

Vasy, András

Astérisque, no. 262 (2000) , 157 p.

MR Zbl | 5 citations dans Numdam

@book{AST_2000__262__R1_0,
     author = {Vasy, Andr\'as},
     title = {Propagation of singularities in three-body scattering},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {262},
     year = {2000},
     mrnumber = {1744795},
     zbl = {0941.35001},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2000__262__R1_0/}
}

TY  - BOOK
AU  - Vasy, András
TI  - Propagation of singularities in three-body scattering
T3  - Astérisque
PY  - 2000
IS  - 262
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2000__262__R1_0/
LA  - en
ID  - AST_2000__262__R1_0
ER  -

%0 Book
%A Vasy, András
%T Propagation of singularities in three-body scattering
%S Astérisque
%D 2000
%N 262
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2000__262__R1_0/
%G en
%F AST_2000__262__R1_0

Vasy, András. Propagation of singularities in three-body scattering. Astérisque, no. 262 (2000), 157 p. http://numdam.org/item/AST_2000__262__R1_0/

Bibliographie
Cité par

[1] P. Blanchard & L. Streit (eds.) - Dynamics and processes, Lect. Notes in Math., Springer-Verlag, 1983. | MR | DOI

[2] A. Bommier - Propriétés de la matrice de diffusion, $2$ -amas $2$ -amas, pour les problèmes à $N$ corps à longue portée, Ann. Inst. H. Poincaré 59 (1993), p. 237-267. | MR | Zbl | EuDML | Numdam

[3] T. Christiansen - Scattering theory for perturbed stratified media, J. Anal. Math. 76 (1998), p. 1-43. | MR | Zbl | DOI

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

[5] V. Enss - Completeness of three-body quantum scattering, in Dynamics and processes [1], p. 68-83. | Zbl

[6] V. Enss, Quantum scattering theory two- and three-body systems with potentials of short and long range, in Schrödinger operators [12], p. 39-176. | MR | Zbl

[7] L. D. Faddeev - Mathematical aspects of the three-body problem in the quantum scattering theory, Steklov Institute, 1963. | Zbl | MR

[8] R. G. Froese & I. Herbst - Exponential bounds and absence of positive eigenvalues of $N$ -body Schrödinger operators, Comm. Math. Phys. 87 (1982), p. 429-447. | MR | Zbl | DOI

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

[10] C. Gérard, H. Isozaki & E. Skibsted - Commutator algebra and resolvent estimates, in Spectral and scattering theory and related topics [42], p. 69-82. | MR | Zbl

[11] G. M. Graf - Asymptotic completeness for $N$ -body short range systems : a new proof, Comm. Math. Phys. 132 (1990), p. 73-101. | MR | Zbl | DOI

[12] S. Graffi (ed.) - Schrödinger operators, Lect. Notes in Math., Springer-Verlag, 1985. | MR | Zbl | DOI

[13] A. Hassell - Distorted plane waves for the $3$ body Schrödinger operator, Geom. Funct. Anal., to appear. | MR | Zbl

[14] A. Hassell, Scattering matrices for the quantum $3$ -body problem, Trans. Amer. Math. Soc., to appear. | MR | Zbl

[15] B. Helffer & J. Sjöstrand - Équation de Schrödinger avec champ magnétique et équation de Harper, Schrödinger operators : Proceedings, Nordic Summer School in Mathematics, Sonderborg, Denmark, 1988. | Zbl | Numdam

B. Helffer & J. Sjöstrand - Équation de Schrödinger avec champ magnétique et équation de Harper, Schrödinger operators : Proceedings, Nordic Summer School in Mathematics, Sonderborg, Denmark, 1989, p. 118-197. | MR | Zbl | DOI

[16] I. Herbst & E. Skibsted - Free channel Fourier transform in the long range $N$ -body problem, J. Analyse Math. 65 (1995), p. 297-332. | MR | Zbl | DOI

[17] L. Hörmander - Fourier integral operators, I, Acta Math. 127 (1971), p. 79-183. | MR | Zbl | DOI

[18] L. Hörmander, The analysis of linear partial differential operators, vol. 1-4, Springer-Verlag, 1983. | Zbl

[19] M. Ikawa (ed.) - Spectral and scattering theory, Lecture Notes in Pure and Applied Math., vol. 161, Marcel Dekker, Inc., New York, 1994. | MR | Zbl

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

[21] H. Isozaki, Asymptotic properties of generalized eigenfunctions for three body Schrödinger operators, Comm. Math. Phys. 153 (1993), p. 1-21. | MR | Zbl | DOI

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

[23] R. Mazzeo & R. B. Melrose - Pseudodifferential operators on manifolds with fibred boundaries, Asian J. Math. 2 (1998), p. 833-866. | MR | Zbl | DOI

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

[25] R. B. Melrose, Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces, in Spectral and scattering theory [19], p. 85-130. | MR | Zbl

[26] R. B. Melrose, Geometric scattering theory, Cambridge University Press, 1995. | MR | Zbl

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

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

[29] R. B. Melrose & M. Zworski - Scattering metrics and geodesic flow at infinity, Invent Math. 124 (1996), p. 389-436. | MR | Zbl | DOI

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

[31] E. Mourre, Operateurs conjugés et propriétés de propagation, Comm. Math. Phys. 91 (1983), p. 279-300. | MR | Zbl | DOI

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

[33] R. T. Seeley - Complex powers of an elliptic operator, Singular Integrals, Proc. of Symposia in Pure Math., vol. 10, American Mathematical Society, 1967, p. 288-307. | MR | Zbl | DOI

[34] I. M. Sigal & A. Soffer - $N$ -particle scattering problem : asymptotic completeness for short range systems, Ann. of Math. 125 (1987), p. 35-108. | MR | Zbl | DOI

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

[36] J. Sjöstrand - Propagation of analytic singularities for second order Dirichlet problems, Comm. Partial Differential Equations 5 (1980), p. 41-94. | MR | Zbl | DOI

[37] E. Skibsted - Smoothness of $N$ -body scattering amplitudes, Reviews in Math. Phys. 4 (1992), p. 619-658. | MR | Zbl | DOI

[38] A. Vasy - Asymptotic behavior of generalized eigenfunctions in $N$ -body scattering, J. Func. Anal. 148 (1997), p. 170-184. | MR | Zbl | DOI

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

[40] J. Wunsch - Projections of distributions on manifolds with boundary, Manuscript.

[41] D. Yafaev - Radiation conditions and scattering theory for $N$ -particle Hamiltonians, Comm. Math. Phys. 154 (1993), p. 523-554. | MR | Zbl | DOI

[42] K. Yajima (ed.) - Spectral and scattering theory and related topics, Advanced studies in pure mathematics, vol. 23, 1994. | MR | DOI