Propagation of singularities in many-body scattering

András Vasy[1]

  • [1] Massachusetts Institute of Technology, Department of Mathematics, Cambridge MA (USA)

Annales scientifiques de l'École Normale Supérieure (2001)

  • Volume: 34, Issue: 3, page 313-402
  • ISSN: 0012-9593

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Vasy, András. "Propagation of singularities in many-body scattering." Annales scientifiques de l'École Normale Supérieure 34.3 (2001): 313-402. <http://eudml.org/doc/82545>.

@article{Vasy2001,
affiliation = {Massachusetts Institute of Technology, Department of Mathematics, Cambridge MA (USA)},
author = {Vasy, András},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {scattering Schrödinger equation; propagation of singularities; tempered distributional solutions; many-body Hamiltonian},
language = {eng},
number = {3},
pages = {313-402},
publisher = {Elsevier},
title = {Propagation of singularities in many-body scattering},
url = {http://eudml.org/doc/82545},
volume = {34},
year = {2001},
}

TY - JOUR
AU - Vasy, András
TI - Propagation of singularities in many-body scattering
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2001
PB - Elsevier
VL - 34
IS - 3
SP - 313
EP - 402
LA - eng
KW - scattering Schrödinger equation; propagation of singularities; tempered distributional solutions; many-body Hamiltonian
UR - http://eudml.org/doc/82545
ER -

References

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  1. [1] Bommier A., Propriétés de la matrice de diffusion, Ann. Inst. Henri Poincaré59 (1993) 237-267. Zbl0804.35111MR1276326
  2. [2] Dereziński J., Asymptotic completeness of long-range N-body quantum systems, Ann. Math.138 (1993) 427-476. Zbl0844.47005MR1240577
  3. [3] Dereziński J., Gérard C., Scattering Theory of Classical Quantum N-particle Systems, Springer, 1997. Zbl0899.47007MR1459161
  4. [4] Froese R.G., Herbst I., Exponential bounds, Comm. Math. Phys.87 (1982) 429-447. Zbl0509.35061MR682117
  5. [5] Froese R.G., Herbst I., A new proof of the Mourre estimate, Duke Math. J.49 (1982) 1075-1085. Zbl0514.35025MR683011
  6. [6] Gérard C., Isozaki H., Skibsted E., Commutator algebra resolvent estimates, in: Advanced Studies in Pure Mathematics, Vol. 23, 1994, pp. 69-82. Zbl0814.35086MR1275395
  7. [7] Gérard C., Isozaki H., Skibsted E., N-body resolvent estimates, J. Math. Soc. Japan48 (1996) 135-160. Zbl0851.35101MR1361552
  8. [8] Graf G.M., Asymptotic completeness for N-body short range systems, Comm. Math. Phys.132 (1990) 73-101. Zbl0726.35096MR1069201
  9. [9] Hassell A., Vasy A., Symbolic functional calculus, J. Funct. Anal.173 (2000) 257-283. Zbl0960.58025MR1760615
  10. [10] Helffer B., Sjöstrand J., Équation de Schrödinger avec champ magnétique et équation de Harper. Zbl0641.35015
  11. [11] Hörmander L., Fourier integral operators, Acta Mathematica127 (1971) 79-183. Zbl0212.46601MR388463
  12. [12] Hörmander L., The Analysis of Linear Partial Differential Operators, Vols. 1–4, Springer-Verlag, 1983. Zbl0521.35002
  13. [13] Ikawa M. (Ed.), Spectral and Scattering Theory, Marcel Dekker, 1994. Zbl0798.00016MR1291635
  14. [14] Isozaki H., Structures of S-matrices for three body Schrödinger operators, Comm. Math. Phys.146 (1992) 241-258. Zbl0748.35026MR1165182
  15. [15] Isozaki H., A generalization of the radiation condition of Sommerfeld for N-body Schrödinger operators, Duke Math. J.74 (1994) 557-584. Zbl0811.35107MR1272984
  16. [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. Zbl0813.35068MR1291639
  17. [17] Jensen A., Propagation estimates for Schrödinger-type operators, Trans. Amer. Math. Soc.291 (1) (1985) 129-144. Zbl0577.35089MR797050
  18. [18] Lebeau G., Propagation des ondes dans les variétés à coins, Ann. Scient. Éc. Norm. Sup.30 (1997) 429-497. Zbl0891.35072MR1456242
  19. [19] Mazzeo R., Melrose R.B., Pseudodifferential operators on manifolds with fibred boundaries, Asian J. Math.2 (1998). Zbl1125.58304MR1734130
  20. [20] Melrose R.B., Differential analysis on manifolds with corners, In preparation. Zbl0754.58035
  21. [21] Melrose R.B., Calculus of conormal distributions on manifolds with corners, Internat. Math. Res. Notices3 (1992) 51-61. Zbl0754.58035MR1154213
  22. [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. Zbl0837.35107MR1291640
  23. [23] Melrose R.B., Sjöstrand J., Singularities of boundary value problems. I, Comm. Pure Appl. Math.31 (1978) 593-617. Zbl0368.35020MR492794
  24. [24] Melrose R.B., Sjöstrand J., Singularities of boundary value problems. II, Comm. Pure Appl. Math.35 (1982) 129-168. Zbl0546.35083MR644020
  25. [25] Melrose R.B., Zworski M., Scattering metrics, Inventiones Math.124 (1996) 389-436. Zbl0855.58058MR1369423
  26. [26] Mourre E., Absence of singular continuous spectrum of certain self-adjoint operators, Comm. Math. Phys.78 (1981) 391-408. Zbl0489.47010MR603501
  27. [27] Perry P., Sigal I.M., Simon B., Spectral analysis of N-body Schrödinger operators, Ann. Math.114 (1981) 519-567. Zbl0477.35069MR634428
  28. [28] Sigal I.M., Soffer A., N-particle scattering problem, Ann. Math.125 (1987) 35-108. Zbl0646.47009MR898052
  29. [29] Sigal I.M., Soffer A., Long-range many-body scattering, Inventiones Math.99 (1990) 115-143. Zbl0702.35197MR1029392
  30. [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. Zbl0853.70010
  31. [31] Sigal I.M., Soffer A., Asymptotic completeness of N-particle long-range scattering, J. Amer. Math. Soc.7 (1994) 307-334. Zbl0811.35091MR1233895
  32. [32] Sjöstrand J., Propagation of analytic singularities for second order Dirichlet problems, Comm. PDE5 (1980) 41-94. Zbl0458.35026MR556454
  33. [33] Skibsted E., Smoothness of N-body scattering amplitudes, Rev. Math. Phys.4 (1992) 619-658. Zbl0781.35047MR1197552
  34. [34] Taylor M., Grazing rays, Comm. Pure Appl. Math.29 (1976) 1-38. Zbl0318.35009MR397175
  35. [35] Vasy A., Asymptotic behavior of generalized eigenfunctions in N-body scattering, J. Funct. Anal.148 (1997) 170-184. Zbl0884.35110MR1461498
  36. [36] Vasy A., Propagation of singularities in three-body scattering, Ph.D. Thesis, Massachusetts Institute of Technology, 1997. Zbl0941.35001
  37. [37] Vasy A., Structure of the resolvent for three-body potentials, Duke Math. J.90 (1997) 379-434. Zbl0891.35111MR1484859
  38. [38] Vasy A., Geometric scattering theory for long-range potentials, Int. Math. Res. Notices1998 (1998) 285-315. Zbl0922.58085MR1616722
  39. [39] Vasy A., Scattering matrices in many-body scattering, Comm. Math. Phys.200 (1999) 105-124. Zbl0929.47044MR1671912
  40. [40] Vasy A., Propagation of singularities in three-body scattering, Astérisque262 (2000). Zbl0941.35001MR1744795
  41. [41] Wang X.P., Microlocal estimates for N-body Schrödinger operators, J. Fac. Sci. Univ. Tokyo Sect. IA, Math.40 (1993) 337-385. Zbl0810.35073MR1255046
  42. [42] Yafaev D., Radiation conditions, Comm. Math. Phys.154 (1993) 523-554. Zbl0781.35048MR1224090

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