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

MSC:
34L99Ordinary differential operators
47E05Ordinary differential operators
34B30Special ODE (Mathieu, Hill, Bessel, etc.)
WorldCat.org
Full Text: DOI
References:
[1] Arnold, V.: Classical mechanics. (1978) · Zbl 0386.70001
[2] Eastham, M. S. P.: The spectral theory of periodic differential equations. (1974) · 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. Harrell, Amer. J. Math., to appear.
[7] E. Harrell, private communication.
[8] Hochstadt, H.: Proc. amer. Math. soc.. 14, 930-932 (1963)
[9] Kato, T.: Perturbation theory for linear operators. (1966) · Zbl 0148.12601
[10] Levitan, B. M.; Sargstan, I. S.: Introduction to spectral theory. (1975)
[11] Magnus, W.; Winkler, W.: Hill’s equation. (1966) · Zbl 0158.09604
[12] Read, M.; Simon, B.: Methods of modern mathematical physics. IV. analysis of operators. (1978) · Zbl 0401.47001
[13] Trubowitz, E.: Comm. pure appl. Math.. 30, 321-337 (1977)
[14] Levy, D.; Keller, J.: Comm. pure appl. Math.. 16, 469-476 (1963)