On the genericity of nonvanishing instability intervals in periodic Dirac systems

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1. [1] N.I. Ahiezer, K spektral'noi teorii uravnenija Lame, Istor.-Mat. Issled., Vol. 23, 1978, pp. 77-86. 
2. [2] J. Avron and B. Simon, Almost Periodic Schrödinger Operators: I. Limit Periodic Potentials, Comm. Math. Phys., Vol. 82, 1981, pp. 101-120. Zbl0484.35069MR638515
3. [3] G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math., Vol. 78, 1946, pp. 1-96. Zbl0063.00523MR15185
4. [4] C.J. Bouwkamp, A Note on Mathieu Functions, Indag. Math., Vol. 10, 1948, pp. 319- 321. Zbl0031.12103MR29008
5. [5] G. Choquet, Lectures on Analysis I, Integration and Topological Vector Spaces, W. A. Benjamin, New York, Amsterdam, 1969. Zbl0181.39601
6. [6] M.S.P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh, 1973. Zbl0287.34016
7. [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. Zbl48.1263.02JFM48.1263.02
8. [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. Zbl52.0461.03JFM52.0461.03
9. [9] E.L. Ince, Further Investigations into the Periodic Lamé Functions, Proc. Roy. Soc. Edinburgh, Vol. 60, 1940, pp. 83-99. Zbl0027.21201MR2400
10. [10] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin etc., 1966. Zbl0148.12601
11. [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. Zbl0028.35803MR9790
12. [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. Zbl56.1049.01JFM56.1049.01
13. [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. Zbl0477.34018MR630951
14. [14] K.M. Schmidt, On the Essential Spectrum of Dirac Operators with Spherically Symmetric Potentials, Math. Ann. (to appear). Zbl0796.35120MR1238410
15. [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. Zbl0346.34015MR473321
16. [16] J. Weidmann, Spectral Theory of Ordinary Differential Operators, Springer Lecture Notes Math., 1258, Springer, Berlin etc., 1987. Zbl0647.47052MR923320