Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique

Mouez Dimassi

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 61, Issue: 2, page 189-204
  • ISSN: 0246-0211

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Dimassi, Mouez. "Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique." Annales de l'I.H.P. Physique théorique 61.2 (1994): 189-204. <http://eudml.org/doc/76653>.

@article{Dimassi1994,
author = {Dimassi, Mouez},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {periodic Schrödinger operator; large-coupling constant limit; asymptotic expansion; essential spectrum},
language = {fre},
number = {2},
pages = {189-204},
publisher = {Gauthier-Villars},
title = {Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique},
url = {http://eudml.org/doc/76653},
volume = {61},
year = {1994},
}

TY - JOUR
AU - Dimassi, Mouez
TI - Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 61
IS - 2
SP - 189
EP - 204
LA - fre
KW - periodic Schrödinger operator; large-coupling constant limit; asymptotic expansion; essential spectrum
UR - http://eudml.org/doc/76653
ER -

References

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  2. [Bi] M. Sh. Birman: [1] Discret spectrum in the gap of the continuous one in the large coupling limit, Oper. Theory: Adv. Appl., Vol. 46, 1990, pp. 17-25.[2] The discret spectrum in a gap of the perturbed periodic operator at large coupling constants, Proc. Conf. Rigorous Results in Quantum Dynamics, Liblice Castle, June 11-15, 1990 (to appear).[3] On discret spectrum in gaps of a perturbed periodic second order operator, Funktional Anal i Prilozken (to appear). MR1124649
  3. [B-S] M.S. Birman and M.Z. Solomyak: [1] Estimates for the singular numbers of integral operators, Uspekhi Mat. Nank., Vol. 32, 1977, pp. 17-84,English trans. in Russian Math. Surveys, Vol. 32, 1977, pp. 15-89.[2] Asymptotic behaviour of the spectrum of pseudo-differential operators with anisotropically homogeneous symbols, I, Vestnik Leningrad Uni. Math. Mekh. Astronom., 1977, n° 13, pp. 3-21; II, 1989, n° 3, 5, 10; English trans. in Vestnik Leningrad Univ. Math., Vol. 10, 1982; Vol. 12, 1980.[3] Negative discret spectrum of the Schrödinger operator with large coupling constant: a qualitative discussion, Ope. Theory: Adv. App., Vol. 46, 1990, pp. 3-16.[4] Schrôdinger operator. Estimates for the number of the bound states as a function-theoretic problem, Lectures of the XIV School on operator theory and Funciton Spaces, I, Novgorod, 1990; English trans., Amer. Math. Soc., Providence RI (to appear).[5] Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations, Advances in Soviet Mathematics, Vol. 7, 1991. MR438186
  4. [D-H] P.A. Deift and R. Hempel, On the existence of eigenvalue of the Schrödinger operator (H - λW) in a spectral gap of, Comm. Math. Phys., Vol. 103, 1986, pp. 461-490. Zbl0594.34022MR832922
  5. [Di] M. Dimassi, Développements asymptotiques des perturbations lentes de l'opérateur de Schrôdinger périodique, à paraître dans Comm. in P.D.E., 1993. Zbl0784.35071
  6. [G-S] F. Gesztesy, B. Simon, On a theorem of Deift and Hempel, Comm. Math. Phys., Vol. 118, 1988, pp. 597-634. Zbl0647.35063MR962490
  7. [He-Sj] B. Helffer, J. Sjöstrand, Équation de Schrödinger avec champ magnétique fort et équation de Harper, Preprint Juin 1988. 
  8. [H] R. Hempel, On the asymptotic distribution of the eigenvalue branches of a Schrödinger operator (H - λW) in a spectral gap of H, J. Reine Angew. Math., Vol. 399, 1989, pp. 38-59. Zbl0681.35066MR1004132
  9. [K-M] W. Kirsh, F. Martinelli, On the density of states of Schrödinger operators with a random potential, J. Phys. A. Math. Gen., Vol. 15, 1982, pp. 2139-2156. Zbl0492.60055MR665829
  10. [Re-Si] M. Reed, B. Simon, Methods of modern mathematical physics, I-IV, Academic Press, pp. 1974-1979. MR751959
  11. [Sh] M.A. Shubin, The spectral theory and the index of elliptic operators with almost periodic-coefficients, Russian Math. Surveys, Vol. 34, 1979, pp. 109-157. Zbl0448.47032MR535710
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  13. [So] A.V. Sobolev, Weyl asymptotics for the discret spectrum of the perturbed Hill operator, Advances in Soviet Mathematics, Vol. 7, 1991, pp. 159-178. Zbl0752.34046MR1306512

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