Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill
Grigis, Alain
Annales scientifiques de l'École Normale Supérieure, Tome 20 (1987), p. 641-672 / Harvested from Numdam
@article{ASENS_1987_4_20_4_641_0,
     author = {Grigis, Alain},
     title = {Estimations asymptotiques des intervalles d'instabilit\'e pour l'\'equation de Hill},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {20},
     year = {1987},
     pages = {641-672},
     doi = {10.24033/asens.1548},
     mrnumber = {89e:34056},
     zbl = {0644.34021},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1987_4_20_4_641_0}
}
Grigis, Alain. Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill. Annales scientifiques de l'École Normale Supérieure, Tome 20 (1987) pp. 641-672. doi : 10.24033/asens.1548. http://gdmltest.u-ga.fr/item/ASENS_1987_4_20_4_641_0/

[1] J. Avron et B. Simon, The Asymptotics of the Gap in the Mathieu Equation (Annals of Physics, vol. 134, 1981, p. 76-84). | MR 82h:34030 | Zbl 0464.34020

[2] M. S. P. Eastham, The Spectral Theory of Periodic Differential Equation, Scottish Academic Press, 1973. | Zbl 0287.34016

[3] J. Ecalle, Cinq applications des fonctions résurgentes, Prépublications d'Orsay, 1984.

[4] M. A. Evgrafov et M. V. Fedoryuk, Asymptotic Behaviour as λ → ∞ of the Solutions of the Equation W''(z) - p(z, λ) W(z) = 0 in the Complex z-Plane (Russian Math. Surveys, vol. 21, 1966, p. 1-48). | Zbl 0173.33801

[5] J. Garnett et E. Trubowitz, Gaps and Bands of One Dimensional Periodic Schrödinger Operators (Comment. Math. Helvetici, vol. 59, 1984, p. 258-312). | MR 85i:34004 | Zbl 0554.34013

[6] C. Gerard et A. Grigis, Precise Estimates of Tunneling and Eigenvalues Near a Potential Barrier [Journal of Differential Equations (à paraître)]. | Zbl 0668.34022

[7] A. Grigis, Sur l'équation de Hill analytique (Séminaire Bony-Sjöstrand-Meyer, 1984-1985, École Polytechnique, exposé n° 16). | Numdam | Zbl 0567.34023

[8] A. Grigis, Estimations asymptotiques des valeurs propres de l'équation de Hill polynomiale (Actes des Journées E.D.P. de Saint-Jean-de-Monts, 1986, conférence n° 7). | Numdam | MR 874549 | Zbl 0602.34016

[9] E. M. Harrel Ii, On the Effect of the Boundary Conditions on the Eigenvalue of Ordinary Differential Equations (American J. of Math., supplement 1981, dedicated to P. Hartman, Baltimore John Hopkins Press). | Zbl 0544.34014

[10] H. P. Mackean et E. Trubowitz, Hill's Operator and Hyperelliptic Function Theory in the Presence of Infinitely Many Branch Points, C.P.A.M., vol. 29, 1976, p. 143-226). | MR 55 #761 | Zbl 0339.34024

[11] W. Magnus et S. Winkler, Hill's Equation, Interscience Publishers, 1966. | MR 33 #5991 | Zbl 0158.09604

[12] F. Pham, Introduction à la résurgence quantique (Exposé au Séminaire Bourbaki, novembre 1985). | Numdam

[13] M. Reed et B. Simon, Methods of Modern Mathematical Physics, IV, Academic Press, 1978. | MR 58 #12429c | Zbl 0401.47001

[14] Y. Sibuya, Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient, North Holland, 1975. | MR 58 #6561 | Zbl 0322.34006

[15] E. Trubowitz, The Inverse Problem for Periodic Potentials (C.P.A.M., vol. 30, 1977, p. 321-337). | MR 55 #3408 | Zbl 0403.34022

[16] A. Voros, The Return of the Quartic Oscillator. The Complex WKB Method (Ann. Inst. Henri Poincaré, vol. 29, n° 3, 1983, p. 211-338). | Numdam | MR 86m:81051 | Zbl 0526.34046

[17] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Krieger, 1976. | MR 57 #812