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On the determination of a Hill’s equation from its spectrum. (English) Zbl 0128.31201


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[1] Coddington, E. A., & N. Levinson, Theory of Ordinary Differential Equations, p. 2l6ff. New York: McGraw-Hill 1955. · Zbl 0064.33002
[2] Hochstadt, H., Function theoretic properties of the discriminant of Hill’s equation. Math. Zeit. 82, 237–242 (1963). · Zbl 0127.04203 · doi:10.1007/BF01111426
[3] Magnus, W., & A. Shenitzer, Hill’s equation. Part I, General theory. New York University, Division of Electromagnetic Research. Research Report Br-22 (1957).
[4] Ambarzumian, V., Über eine Frage der Eigenwerttheorie. Zeit. f. Physik 53, 690–695 (1929). · JFM 55.0868.01 · doi:10.1007/BF01330827
[5] Borg, G., Eine Umkehrung der Sturm-Liouvillschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte. Acta Math. 78, 1–96 (1946). · Zbl 0063.00523 · doi:10.1007/BF02421600
[6] Hochstadt, H., Asymptotic estimates of the Sturm-Liouville spectrum. Comm. Pure and Applied Math. 14, 749–764 (1961). · Zbl 0102.07403 · doi:10.1002/cpa.3160140408
[7] Ungar, P., Stable Hill equations. Comm. Pure and Applied Math. 14, 707–710 (1961). · Zbl 0123.05005 · doi:10.1002/cpa.3160140403
[8] Erdélyi, A., Higher Transcendental Functions, Vol. III., p. 63ff. New York: McGraw-Hill 1955. · Zbl 0064.06302
[9] Magnus, W., & S. Winkler, Hill’s Equation, Part II, Transformations, Approximations, Examples, New York University. Division of Electromagnetic Research. Research Report Br-38 (1961).
[10] Hochstadt, H., Results, old and new, in the theory of Hill’s equation. Trans. N.Y. Acad. Sci., Ser. II, 26, 887–901 (1964). · doi:10.1111/j.2164-0947.1964.tb02962.x
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