Semiclassical resolvent estimates for two and three-body Schrödinger operators

Christian Gérard

Journées équations aux dérivées partielles (1989)

  • page 1-10
  • ISSN: 0752-0360

How to cite


Gérard, Christian. "Semiclassical resolvent estimates for two and three-body Schrödinger operators." Journées équations aux dérivées partielles (1989): 1-10. <>.

author = {Gérard, Christian},
journal = {Journées équations aux dérivées partielles},
keywords = {Resolvent estimates; semiclassical limit; three-body Schrödinger operators; commutator; escape function},
language = {eng},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {Semiclassical resolvent estimates for two and three-body Schrödinger operators},
url = {},
year = {1989},

AU - Gérard, Christian
TI - Semiclassical resolvent estimates for two and three-body Schrödinger operators
JO - Journées équations aux dérivées partielles
PY - 1989
PB - Ecole polytechnique
SP - 1
EP - 10
LA - eng
KW - Resolvent estimates; semiclassical limit; three-body Schrödinger operators; commutator; escape function
UR -
ER -


  1. [Ag] S. Agmon : Lectures on exponential decay of solutions to second order elliptic equations. Princeton University Press (1982). Zbl0503.35001
  2. [B-C-D] P. Briet, J-M. Combes, P. Duclos : On the location of resonances of Schrödinger operators in the semiclassical limit I. Resonances free domains, J. of Math. Anal. and Appl. Vol. 126, n° 1 (1987), 90-99. Zbl0629.47043MR89e:81028a
  3. [C-F-K-S] H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon : Schrödinger operators with applications to quantum mechanics and global geometry. Texts and Monographs in Physics, Springer Verlag (1987). Zbl0619.47005
  4. [De] J. Derezinski : A new proof of propagation Theorem for N-body quantum system. Preprint (1988). 
  5. [F-H] R.G. Froese, I. Herbst : A new proof of Mourre estimate, Duke Math. J. Vol. 49, n° 4 (1982), 1075-1085. Zbl0514.35025MR85d:35092
  6. [Ge-Ma] Ch. Gérard, A. Martinez : Principe d'absorption limite pour des opérateurs de Schrödinger à longue portée. C.R. Acad. Sci. Paris t.306, série I (1988), 121-123. Zbl0672.35013
  7. [Ge-Sj] Ch. Gérard, J. Sjöstrand : Semiclassical resonances generated by a closed trajectory of hyperbolic type. Comm. in Math. Phys. 108 (1987), 391-421. Zbl0637.35027MR88k:58151
  8. [He-Ro] B. Helffer, D. Robert : Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles. J. Funct. Anal. 53 (1983), 246-268. Zbl0524.35103MR85i:47052
  9. [He-Sj] B. Helffer, J. Sjöstrand : Résonances en limite semiclassique. Bull. de la S.M.F. mémoire n° 24/25, tome 114 (1986). Zbl0631.35075
  10. [H-N] P. Hislop, S. Nakamura : Semiclassical resolvent estimates. Preprint (1988). Zbl0719.35064
  11. [Hö] L. Hörmander : The analysis of linear partial differential operators III, Springer Verlag Berlin Heidelberg New York Tokyo (1985). Zbl0601.35001
  12. [Je] A. Jensen : High energy resolvent estimates for generalized many body Schrödinger operators. Preprint (1988). 
  13. [M] E. Mourre : Absence of singular continuous spectrum for certain selfadjoint operators. Comm. in Math. Phys. 78 (1981), 391-408. Zbl0489.47010MR82c:47030
  14. [P-S-S] P. Perry, I.M. Sigal, B. Simon : Spectral analysis of N- body Schrödinger operators. Ann. of Math. 114 (1981), 519-567. Zbl0477.35069MR83b:81129
  15. [Ro] D. Robert : Autour de l'approximation semiclassique, Birkhaüser (1983). Zbl0621.35001
  16. [Ro-Ta1] D. Robert, H. Tamura : Semiclassical estimates for resolvents of Schrödinger operators and asymptotics for total scattering cross sections. Ann. I.H.P. 46 (1987), 415-442. Zbl0648.35066MR89b:81041
  17. [Ro-Ta2] D. Robert, H. Tamura : Asymptotic behavior of Schrödinger operators scattering amplitudes in semiclassical and low energy limits. Preprint (1988). 
  18. [Sj] J. Sjöstrand : Private communication. 
  19. [Wa1] X.P. Wang : Asymptotiques semiclassiques pour les opérateurs de Schrödinger et de Dirac. Thèse d'Etat (1986). 
  20. [Wa2] X.P. Wang : Semiclassical estimates on resolvents of Schrödinger operators with homogeneous electric field. Preprint (1988). 

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