Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée
Annales de l'I.H.P. Physique théorique, Volume 51 (1989) no. 1, p. 81-110
@article{AIHPA_1989__51_1_81_0,
     author = {G\'erard, Christian and Martinez, Andr\'e},
     title = {Prolongement m\'eromorphe de la matrice de scattering pour des probl\`emes \`a deux corps \`a longue port\'ee},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {1},
     year = {1989},
     pages = {81-110},
     zbl = {0711.35097},
     mrnumber = {1029851},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPA_1989__51_1_81_0}
}
Gérard, Christian; Martinez, André. Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée. Annales de l'I.H.P. Physique théorique, Volume 51 (1989) no. 1, pp. 81-110. http://www.numdam.org/item/AIHPA_1989__51_1_81_0/

[Ag] S. Agmon, Spectral Theory Schrôdinger Operators on Euclidean and non-Euclidean Spaces, Comm. Pure Appl. Math., vol. 39, 1986, p. 53-516. | MR 861480 | Zbl 0601.47039

[Ag-Co] J. Aguilar et J.-M. Combes, A class of Analytic perturbations for One-Body Schrôdinger Hamiltonians, Comm. Math. Phys., vol. 22, 1971, p. 269-279. | MR 345551 | Zbl 0219.47011

[Ag-Kl] S. Agmon et M. Klein, Exposé au colloque d'analyse microlocale d'Oberwolfach, 1987.

[B-B] D. Babbit et E. Balslev, Local Distorsion Techniques and the Unitary of the S-Matrix for the Two-Body Problem, J. Math. Anal. Appl., vol. 54, 1976, p. 316-349. | MR 413860

[B1] E. Balslev, Analytic Scattering Theory for Two-Body Schrôdinger Operators, J. Funt. Anal., vol. 29, 1978, p. 375-396. | MR 512251 | Zbl 0392.47003

[B2] E. Balslev, Local Spectral Deformation Techniques for Schrôdinger Operators, J. Funt. Anal., vol. 58, 1984, p. 79-105. | MR 756770 | Zbl 0556.35033

[B3] E. Balslev, Analytic Scattering Theory of Quantum Mechanical Three-Body Systems, Ann. I.H.P., section A, vol. 23, 1980, p. 125-160. | Numdam | MR 580324 | Zbl 0428.47003

[B4] E. Balslev, Analytic Scattering Theory for Many-Body Systems Below the Smallest Three-Body Threshold, Comm. Math. Phys., vol. 77, 1980, p. 173- 210. | MR 589431 | Zbl 0453.47002

[Ba-Co] E. Balslev et J.-M. Combes, Spectral Properties of Many-Body Schrödinger Operators with Dilation-Analytic Interactions, Comm. Math. Phys., vol. 22, 1971, p. 280-294. | MR 345552 | Zbl 0219.47005

[Ba] T. Bang, On Quasi-analytische Funktionen, Thèse, Univ. de Copenhague, 1946.

[Ca-Za] L. Cattabriga et L. Zanghirati, Fourier Integral Operators of Infinite Order on Gevrey Spaces. Applications to the Cauchy Problem for Hyperbolic Operators, in Advances in Microlocal Analysis, série C, vol. 168, Nato ASI Series, 1985. | Zbl 0601.35065

[Cy] H.L. Cycon, Resonances Defined by Modified Dilations, Helv. Phys. Acta, vol. 58, 1985, p. 969-981. | MR 821113

[De] J. Derezinski, Existence and Analyticity of Many-Body Scattering Amplitudes at low Energies, J. Math. Phys., vol. 28, 1987, p. 1080-1088. | MR 887027 | Zbl 0636.35080

[Ge-Ma] C. Gérard et A. Martinez, Semiclassical Asymptotics for the Spectral Function of Long range Schrôdinger Operators, J. Funct. Anal., vol. 84, n° 1, 1989, p. 226-254. (Voir aussi exposé des Actes du colloque E.D.P. de Saint-Jean-de-Monts, 1987). | MR 999499 | Zbl 0692.35069

[Ha] G. Hagedorn, A Link Between Scattering Resonances and Dilation Analytic Resonances in Few-Body Quantum Mechanics, Comm. Math. Phys., vol. 65, 1979, p. 181-188. | MR 528190 | Zbl 0404.47007

[He-Ma] B. Helffer et A. Martinez, Comparaison entre les diverses notions de résonances, Helv. Phys. Acta, vol. 60, 1987, p. 992-1003. | MR 929933

[He-Sj] B. Helffer et J. Sjöstrand, Resonances en limite semiclassique, Bull. S.M.F., mémoires n° 24/25, 114, 1986.

[Hö] L. Hormander, An Introduction to Complex Analysis in Several Variables, North-Holland, 1973. | MR 344507

[Hu] W. Hunziker, Distorsion Analycicity and Molecular Resonances Curves, Ann. I.H.P., Section A, 1986. | Numdam

[I] H. Isozaki, Differentiability of Generalized Fourier Transform Associated with Schrôdinger Operators, J. Math. Kyoto Univ., vol. 25, 1985, p. 789-806. | MR 810981 | Zbl 0612.35004

[I-K1] H. Isozaki et H. Kitada, Modified wave operators with time independent modifiers, J. Fac. Sci. Tokyo Univ., Sect. 1A, 32, 1985, p. 77-104. | MR 783182 | Zbl 0582.35036

[I-K2] H. Isozaki et H. Kitada, Scattering Matrices for Two-Body Schrôdinger Operators. Scientific Papers of the College of Arts and Sciences, Tokyo Univ., vol. 35, 1985, p. 81-107. | MR 847881 | Zbl 0615.35065

[Je] A. Jensen, Local Distorsion Techniques, Resonances and Poles of the S-Matrix, J. Math. Anal. Appl., vol. 59, 1977, p. 505-513. | MR 441153 | Zbl 0361.47018

[Ku] S.T. Kuroda, An Introduction to Scattering Theory, Aarhus Univ. Lecture Notes, n° 51, 1978. | MR 528757 | Zbl 0407.47003

[La-Li] L. Landau et E. Lifchitz, Mécanique quantique, théorie non relativiste, Mir éd., 1967.

[La] P. Laubin, Analyse microlocale des singularités analytiques, Bull. Soc. Roy. Sci. Liège, vol. 52, 1983, p. 103-212. | MR 720427 | Zbl 0567.58028

[L-P] P.D. Lax et R.S. Phillips, Scattering Theory, Academic Press, 1967. | MR 217440 | Zbl 0186.16301

[Re-Si] M. Reed et B. Simon, Methods of Modern Mathematical Physics, vol. III et IV, Academic Press, 1978.

[Ro] C. Roumieu, Sur quelques extensions de distributions, Ann. Sci. Ec. Norm. Sup., 3e série, t. 77, 1960, p. 41-121. | Numdam | MR 121643 | Zbl 0104.33403

[S-T] N. Shenk et D. Thoe, Resonant states and poles of the scattering matrix for perturbations of -Δ, J. Math. Anal. Appl., vol. 54, 1976, p. 316-349. | MR 308616

[Si1] I.M. Sigal, Scattering Theory for Many-Body Systems-Rigorous Results, Lect. Notes in Math., n° 1011, Springer, 1983. | MR 715786

[Si2] I.M. Sigal, Analytic Properties of the Scattering Matrix of Many Particle Systems, Integral Equations and Operator Theory, vol. 9, 1986, p. 134-153. | MR 824624 | Zbl 0605.47009

[Sim1] B. Simon, The Definition of Molecular Resonances Curves by the Method of Exterior Complex Scaling, Phys. Lett., vol. 71A, 1979, p. 211-214.

Sim2] B. Simon, Resonances in N-Body Quantum Systems with Dilation-Analytic Potentials and the Foundation of Time-Dependent Perturbation Theory, Ann. Math., vol. 97, 1973, p. 247-272. | MR 353896 | Zbl 0252.47009

[Sj] J. Sjöstrand, Singularités analytiques microlocales, Astérisque, vol. 95, 1982. | MR 699623 | Zbl 0524.35007