On the genericity of nonvanishing instability intervals in periodic Dirac systems
Annales de l'I.H.P. Physique théorique, Tome 59 (1993) no. 3, pp. 315-326.
@article{AIHPA_1993__59_3_315_0,
     author = {Schmidt, Karl Michael},
     title = {On the genericity of nonvanishing instability intervals in periodic Dirac systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {315--326},
     publisher = {Gauthier-Villars},
     volume = {59},
     number = {3},
     year = {1993},
     zbl = {0794.34076},
     mrnumber = {1276329},
     language = {en},
     url = {archive.numdam.org/item/AIHPA_1993__59_3_315_0/}
}
Schmidt, Karl Michael. On the genericity of nonvanishing instability intervals in periodic Dirac systems. Annales de l'I.H.P. Physique théorique, Tome 59 (1993) no. 3, pp. 315-326. http://archive.numdam.org/item/AIHPA_1993__59_3_315_0/

[1] N.I. Ahiezer, K spektral'noi teorii uravnenija Lame, Istor.-Mat. Issled., Vol. 23, 1978, pp. 77-86.

[2] J. Avron and B. Simon, Almost Periodic Schrödinger Operators: I. Limit Periodic Potentials, Comm. Math. Phys., Vol. 82, 1981, pp. 101-120. | MR 638515 | Zbl 0484.35069

[3] G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math., Vol. 78, 1946, pp. 1-96. | MR 15185 | Zbl 0063.00523

[4] C.J. Bouwkamp, A Note on Mathieu Functions, Indag. Math., Vol. 10, 1948, pp. 319- 321. | MR 29008 | Zbl 0031.12103

[5] G. Choquet, Lectures on Analysis I, Integration and Topological Vector Spaces, W. A. Benjamin, New York, Amsterdam, 1969. | Zbl 0181.39601

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

[7] E.L. Ince, A Proof of the Impossibility of the Coexistence of Two Mathieu Functions, Proc. Camb. Phil. Sol., Vol. 21, 1922, pp. 117-120. | JFM 48.1263.02

[8] E.L. Ince, Periodic Solutions of a Linear Differential Equation of the Second Order with Periodic Coefficients, Proc. Camb. Phil. Soc., Vol. 23, 1927, pp. 44-46. | JFM 52.0461.03

[9] E.L. Ince, Further Investigations into the Periodic Lamé Functions, Proc. Roy. Soc. Edinburgh, Vol. 60, 1940, pp. 83-99. | MR 2400 | Zbl 0027.21201

[10] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin etc., 1966. | Zbl 0148.12601

[11] K. Klotter and G. Kotowski, Über die Stabilität der Lösungen Hillscher Differentialgleichungen mit drei unabhängigen Parametern, Z. Angew. Math. Mech., Vol. 23, 1943, pp. 149-155. | MR 9790 | Zbl 0028.35803

[12] Ž. Marković, Sur les solutions de l'équation différentielle linéaire du second ordre à coefficient périodique, Proc. Lond. Math. Soc., (2), Vol. 31, 1930, pp. 417-438. | JFM 56.1049.01

[13] J. Moser, An Example of a Schrödinger Equation with Almost Periodic Potential and Nowhere Dense Spectrum, Comment. Math. Helv., Vol. 56, 1981, pp. 198-224. | MR 630951 | Zbl 0477.34018

[14] K.M. Schmidt, On the Essential Spectrum of Dirac Operators with Spherically Symmetric Potentials, Math. Ann. (to appear). | MR 1238410 | Zbl 0796.35120

[15] B. Simon, On the Genericity of Nonvanishing Instability Intervals in Hill's Equation, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 24, 1976, pp. 91-93. | Numdam | MR 473321 | Zbl 0346.34015

[16] J. Weidmann, Spectral Theory of Ordinary Differential Operators, Springer Lecture Notes Math., 1258, Springer, Berlin etc., 1987. | MR 923320 | Zbl 0647.47052