Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes

R. de La Bretèche

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 70, Issue: 4, page 369-380
  • ISSN: 0246-0211

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La Bretèche, R. de. "Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes." Annales de l'I.H.P. Physique théorique 70.4 (1999): 369-380. <http://eudml.org/doc/76820>.

@article{LaBretèche1999,
author = {La Bretèche, R. de},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {harmonic oscillator; Schrödinger operator; convex functions},
language = {fre},
number = {4},
pages = {369-380},
publisher = {Gauthier-Villars},
title = {Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes},
url = {http://eudml.org/doc/76820},
volume = {70},
year = {1999},
}

TY - JOUR
AU - La Bretèche, R. de
TI - Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 70
IS - 4
SP - 369
EP - 380
LA - fre
KW - harmonic oscillator; Schrödinger operator; convex functions
UR - http://eudml.org/doc/76820
ER -

References

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  1. [AL78] M. Aizenman et E. Lieb, On semi-classical bounds for eigenvalues of Schrödinger Operators, Phys. Lett.66A, 1978, 427-429. MR598768
  2. [BS96] Ph Blanchard et J. Stubbe, Bound States for Schrödinger Hamiltonians : Phase space methods and applications, Rev. in Math. Physics, vol. 8, n° 4, 1996, 503-548. Zbl0859.35101MR1405763
  3. [HP90] B. Helffer et B. Parisse, Riesz means of bound states and semi classical limit connected with a Lieb-Thirring's conjecture III, Prépublication de l'École Normale supérieure, 1990. 
  4. [HR83] B. Helffer et D. Robert, Calcul fonctionnel par la transformée de Mellin et applications, J. Funct. Anal., 53, 1983, 246-268. Zbl0524.35103MR724029
  5. [HR90-1] B. Helffer et D. Robert, Riesz means of bound states and semi classical limit connected with a Lieb-Thirring's conjecture I, Asymptotic Analysis, 3, 91-103, 1990. Zbl0717.35062MR1061661
  6. [HR90-2] B. Helffer et D. Robert, Riesz means of bound states and semi classical limit connected with a Lieb-Thirring's conjecture II, Ann. Inst. Henri Poincaré, section Physique Théorique, 53 (2), 1990, 139-147. Zbl0728.35078MR1079775
  7. [L97-1] A. Laptev, Dirichlet and Neumann eigenvalue problems on domains in euclidean spaces, J. Funct. Anal., 151, 1997. Zbl0892.35115MR1491551
  8. [L97-2] A. Laptev, On the Lieb-Thirring conjecture for a class of potentials, preprint 1997. MR1747896
  9. [LT76] E.H. Lieb et W.E. Thirring, Inequalities for the moments of the eigenvalues of the Schrödinger equation and their relation to Sobolev inequalities, Studies in Math. Phys., (E. Lieb, B. Simon, A. Wightman Eds), Princeton Univ. Press, 1976, 269-303. Zbl0342.35044
  10. [MU96] H. Matsumoto et N. Ueki, Spectral Analysis of Schrödinger operators with Magnetic Fields, J. Funct. Anal. , 140, n° 1, 218-255. Zbl0866.35083MR1404582

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