Semiclassical resolvent estimates

Peter D. Hislop; Shu Nakamura

Annales de l'I.H.P. Physique théorique (1989)

  • Volume: 51, Issue: 2, page 187-198
  • ISSN: 0246-0211

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Hislop, Peter D., and Nakamura, Shu. "Semiclassical resolvent estimates." Annales de l'I.H.P. Physique théorique 51.2 (1989): 187-198. <http://eudml.org/doc/76464>.

@article{Hislop1989,
author = {Hislop, Peter D., Nakamura, Shu},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {resolvent estimates; semi-classical behaviour; scattering cross-section; commutator},
language = {eng},
number = {2},
pages = {187-198},
publisher = {Gauthier-Villars},
title = {Semiclassical resolvent estimates},
url = {http://eudml.org/doc/76464},
volume = {51},
year = {1989},
}

TY - JOUR
AU - Hislop, Peter D.
AU - Nakamura, Shu
TI - Semiclassical resolvent estimates
JO - Annales de l'I.H.P. Physique théorique
PY - 1989
PB - Gauthier-Villars
VL - 51
IS - 2
SP - 187
EP - 198
LA - eng
KW - resolvent estimates; semi-classical behaviour; scattering cross-section; commutator
UR - http://eudml.org/doc/76464
ER -

References

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  2. [BCD-2] Ph Briet, J.M. Combes et P. Duclos, Spectral Stability Under Tunneling, Marseille preprint CPT-88/P. 2097, to appear in Commun. Math. Phys., 1989. MR1027916
  3. [CFKS] H.L. Cycon, R.G. Froese, W. Kirsch et B. Simon, Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Berlin, Springer-Verlag, 1987. Zbl0619.47005MR883643
  4. [DeBH] S. Debièvre et P.D. Hislop, Spectral Resonances for the Laplace-Beltrami Operator, Ann. Inst. Henri Poincaré, Vol. 48, 1988, pp. 97-104. Zbl0645.58041MR952658
  5. [GM] C. Gérard, A. Martinez, Principe d'absorption limite pour des opérateurs de Schrödinger à longue portée, C.R. Acad. Sci. Paris, T. 306, 1988, pp. 121-123. Zbl0672.35013MR929103
  6. [HeSj] B. Helffer et J. Sjöstrand, Resonances en limite semi-classique, Supplem. Bulletin S.M.F., T. 114, 1986. Zbl0631.35075
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  9. [L] R. Lavine, Absolute Continuity of Positive Spectrum for Schrödinger Operators with Long-Range Potentials, J. Funct. Anal., Vol. 12, 1973, pp. 30-54. Zbl0246.47017MR342880
  10. [M] E. Mourre, Absence of Singular Spectrum for Certain Self-Adjoint Operators, Commun. Math. Phys., Vol. 78, 1981, pp. 391-400. Zbl0489.47010MR603501
  11. [N-1] S. Nakamura, Scattering Theory for the Shape Resonance Model I, II, Ann. Inst. Henri Poincaré, Vol. 50, 1989, pp. 35-52 and 53-62. Zbl0686.35091
  12. [N-2] S. Nakamura, A Note on the Absence of Resonances for Schrödinger Operator, Lett. Math. Phys., Vol. 16, 1988, pp. 217-223. Zbl0688.35073MR967706
  13. [RT-1] D. Robert et H. Tamura, Semiclassical Bounds for Resolvents of Schrödinger Operators and Asymptotics for Scattering Phases, Commun. P.D.E., Vol. 9, 1984, p. 1017-1058. Zbl0561.35021MR755930
  14. [RT-2] D. Robert et H. Tamura, Semiclassical Estimates for Resolvents and Asymptotics for Total Scattering Cross-Sections, Ann. Inst. Henri Poincaré, Vol. 46, 1987, pp. 415-442. Zbl0648.35066MR912158
  15. [S-1] I.M. Sigal, Sharp Exponential Bounds on Resonances States and Width of Resonances, Adv. Appl. Math., Vol. 9, pp. 127-166. Zbl0652.47008MR937519
  16. [S-2] I.M. Sigal, Lectures on Scattering Theory, University of Toronto, 1986. 
  17. [Y] D.R. Yafaev, The Eikonal Approximation and the Asymptotics of the Total Cross-Section for the Schrödinger Equations, Ann. Inst. Henri Poincaré, Vol. 44, 1986, pp. 397-425. Zbl0608.35054MR850898

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