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The asymptotics of the gap in the Mathieu equation. (English) Zbl 0464.34020


MSC:

34L99 Ordinary differential operators
47E05 General theory of ordinary differential operators
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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References:

[1] Arnold, V., (Classical Mechanics (1978), Springer-Verlag: Springer-Verlag Berlin/New York)
[2] Eastham, M. S.P., (The Spectral Theory of Periodic Differential Equations (1974), Hafner: Hafner New York) · Zbl 0285.34015
[3] Harrell, E., Commun. Math. Phys., 60, 73-95 (1978)
[4] Harrell, E., Ann. Phys. (N.Y.), 119, 351-369 (1979)
[5] Harrell, E., Commun. Math. Phys., 75, 239-261 (1980)
[6] E. HarrellAmer. J. Math.; E. HarrellAmer. J. Math.
[7] E. Harrell; E. Harrell
[8] Hochstadt, H., (Proc. Amer. Math. Soc., 14 (1963)), 930-932
[9] Kato, T., (Perturbation Theory for Linear Operators (1966), Springer-Verlag: Springer-Verlag Berlin/New York)
[10] Levitan, B. M.; Sargstan, I. S., (Introduction to Spectral Theory (1975), Amer, Math. Soc: Amer, Math. Soc Providence, R.I)
[11] Magnus, W.; Winkler, W., (Hill’s Equation (1966), Wiley: Wiley New York) · Zbl 0158.09604
[12] Read, M.; Simon, B., (Methods of Modern Mathematical Physics. IV. Analysis of Operators (1978), Academic Press: Academic Press New York)
[13] Trubowitz, E., Comm. Pure Appl. Math., 30, 321-337 (1977)
[14] Levy, D.; Keller, J., Comm. Pure Appl. Math., 16, 469-476 (1963)
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