Une formule de traces pour l’opérateur de Schrödinger dans 3

Yves Colin de Verdière

Annales scientifiques de l'École Normale Supérieure (1981)

  • Volume: 14, Issue: 1, page 27-39
  • ISSN: 0012-9593

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Colin de Verdière, Yves. "Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb {R}^3$." Annales scientifiques de l'École Normale Supérieure 14.1 (1981): 27-39. <http://eudml.org/doc/82065>.

@article{ColindeVerdière1981,
author = {Colin de Verdière, Yves},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {trace formula; Schrödinger operator; Fredholm determinant},
language = {fre},
number = {1},
pages = {27-39},
publisher = {Elsevier},
title = {Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb \{R\}^3$},
url = {http://eudml.org/doc/82065},
volume = {14},
year = {1981},
}

TY - JOUR
AU - Colin de Verdière, Yves
TI - Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb {R}^3$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1981
PB - Elsevier
VL - 14
IS - 1
SP - 27
EP - 39
LA - fre
KW - trace formula; Schrödinger operator; Fredholm determinant
UR - http://eudml.org/doc/82065
ER -

References

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  4. [B-K] M. S. BIRMAN et M. G. KREIN, On the Theory of wave Operators and Scattering Operators (Dokl. Akad. Nauk S.S.S.R., vol. 144, 1962, p. 475-478). Zbl0196.45004MR25 #2447
  5. [CV] Y. COLIN DE VERDIÈRE, Spectre du laplacien et longueurs des géodésiques périodiques II (Compositio Mathematica, vol. 27, 1973, p. 159-184). Zbl0281.53036MR50 #1293
  6. [F-Z] P. FADDEEV et V. ZAKHAROV, KdV Equation : a Completely Integrable Hamiltonian System (Funct. Anal. and Appl. vol. 5, 1971, p. 280-288). Zbl0257.35074
  7. [G-M-G-T] V. GLASER, A. MARTIN, H. GROSSE et W. THIRRING, A Family of Optimal Conditions for the Absence of Bound States in a Potential. Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 169-194. Zbl0332.31004
  8. [J-K] A. JENSEN et T. KATO, Asymptotic behaviour of the Scattering Phase for Exterior Domains (Comm. P.D.E., vol. 3, 1978, p. 1165-1195). Zbl0419.35067MR80g:35098
  9. [K-M] H. P. MCKEAN et VAN MOERBECKE, The Spectrum of Hill's Equation (Invent. Math., vol. 30, 1975, p. 217-254). Zbl0319.34024MR53 #936
  10. [L-P1] P. LAX et R. S. PHILLIPS, Scattering Theory for Automorphic Functions (Annals Math. Studies, 1976, Princeton). Zbl0362.10022MR58 #27768
  11. [L-P 2] P. LAX et R. S. PHILLIPS, The Time Delay Operator and a Related Trace Formula. Topics in Functional Analysis, GOHBERG et M. KAC, ed., Academic Press, 1978, p. 197-215. Zbl0463.47006MR80j:47010
  12. [L-T] E. LIEB et W. THIRRING, Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian... Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 269-304. Zbl0342.35044
  13. [MR] A. MAJDA et J. RALSTON, An Analogue of Weyl's Theorem for Unbounded Domains I, II et III (Duke Math. J., vol. 45, p. 183-196 et 513-536 ; vol. 46, 1979, p. 725-731). Zbl0408.35069
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  19. [Z-K] C. ZEMACH et A. KLEIN, The Born Expansion in non Relativistic Quantum Theory, I (Nuovo Cimento, vol. 10, 1958, p. 1078-1087). Zbl0084.44803MR21 #580

Citations in EuDML Documents

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  1. Hart F. Smith, Maciej Zworski, [unknown]
  2. Jean-Marc Bouclet, Asymptotic behavior of regularized scattering phases for long range perturbations
  3. A. V. Sobolev, Efficient bounds for the spectral shift function
  4. Y. Colin de Verdière, La matrice de Scattering pour l'opérateur de Schrödinger sur la droite réelle
  5. D. Robert, Approximation semi-classique de la phase de diffusion pour un potentiel (d'après un travail de D. Robert et H. Tamura)
  6. D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du laplacien
  7. Gilles Carron, Déterminant relatif et la fonction Xi
  8. Werner Müller, Relative determinants of elliptic operators and scattering theory
  9. Veselin Petkov, Georgi Popov, Asymptotic behaviour of the scattering phase for non-trapping obstacles
  10. D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du second ordre du laplacien

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