Asymptotic estimates for the eigenvalues of the polynomial Hill's equation

Alain Grigis

Journées équations aux dérivées partielles (1986)

  • page 1-7
  • ISSN: 0752-0360

How to cite


Grigis, Alain. "Estimations asymptotiques des valeurs propres de l'équation de Hill polynomiale." Journées équations aux dérivées partielles (1986): 1-7. <>.

author = {Grigis, Alain},
journal = {Journées équations aux dérivées partielles},
keywords = {Hill's equation; WKB method},
language = {fre},
pages = {1-7},
publisher = {Ecole polytechnique},
title = {Estimations asymptotiques des valeurs propres de l'équation de Hill polynomiale},
url = {},
year = {1986},

AU - Grigis, Alain
TI - Estimations asymptotiques des valeurs propres de l'équation de Hill polynomiale
JO - Journées équations aux dérivées partielles
PY - 1986
PB - Ecole polytechnique
SP - 1
EP - 7
LA - fre
KW - Hill's equation; WKB method
UR -
ER -


  1. [1] J. Avron, B. Simon: The asymptotics of the Gap in the Mathieu equation, Annals of Physics 134, (1981) 76-84. Zbl0464.34020MR82h:34030
  2. [2] M.S.P. Eastham: The spectral theory of periodic differential equation, Scottish Academic Press (1973). Zbl0287.34016
  3. [3] J. Ecalle: Cinq applications des fonctions résurgentes, Prépublications d'Orsay (1984). 
  4. [4] C. Gérard, A. Grigis: Precise estimation of tunneling and eigenvalues near a potential barrier, en préparation. Zbl0668.34022
  5. [5] A. Grigis: Sur l'équation de Hill analytique, Séminaire Bony-Meyer-Sjöstrand, Ecole Polytechnique 1984-1985 exposé n° 16. Zbl0567.34023
  6. [6] A. Grigis: A paraître. 
  7. [7] Harrel: Américan J. of Maths, à paraître. 
  8. [8] F. Pham: Introduction à la resurgence quantique. Séminaire Bourbaki 85-86 exposé n° 656. 
  9. [9] Y. Sibuya: Global theory of a second order linear ordinary differential equation with a polynomial coefficient, North Holland (1975). Zbl0322.34006MR58 #6561
  10. [10] A. Voros: The return of the quartic oscillator. The complex WKB method Ann. Inst. Henri Poincaré vol 29 n° 3 (1983) 211-338. Zbl0526.34046MR86m:81051

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