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Hill’s operator and hyperelliptic function theory in the presence of infinitely many branch points. (English) Zbl 0339.34024


MSC:

34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34L99 Ordinary differential operators
35B10 Periodic solutions to PDEs
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References:

[1] The Classical Moment Problem, Hafner Publishing Co., New York, 1965.
[2] Borg, Acta Math. 78 pp 1– (1945)
[3] Les Fonctions Quasi-Analytiques, Gauthier-Villars, Paris, 1926.
[4] Hilbert Spaces of Entire Functions, Prentice-Hall, Englewood Cliffs, N.J., 1968.
[5] Dubrovin, Soviet Math. Dokl. 15 pp 1597– (1974)
[6] Erdelyi, Ann. der Physik 19 pp 585– (1934)
[7] Faddeev, Uspekhi Mat. Nauk. 14 pp 57– (1959)
[8] (English translation: J. Math. Phys. 4 pp 72– (1963)
[9] Flaschka, Arch. Rat. Mech. Anal. (1975)
[10] Discrete and periodic illustrations of some aspects of the inverse method, Dynamical Systems theory and Applications, ed. Springer-Verlag, New York, 1975, pp. 441–446.
[11] Goldberg, J. Math. Anal. Appl. 51 pp 705– (1975)
[12] Hochstadt, Math. Zeit. 82 pp 237– (1963)
[13] Hochstadt, Arch. Rat. Mech. Anal. 19 pp 353– (1965)
[14] Ince, Proc. Roy. Soc. Edin. 60 pp 47– (1940) · Zbl 0027.21103
[15] Ince, Proc. Roy. Soc. Edin. 60 pp 83– (1940) · Zbl 0027.21201
[16] Its, Funct. An. Appl. 9 pp 65– (1975)
[17] Kac, Proc. Nat. Acad. Sci., USA 72 pp 1627– (1975)
[18] Kac, Advances in Math. 16 pp 160– (1975)
[19] Kac, Proc. Nat. Acad. Sci. USA 72 pp 2879– (1975)
[20] Kruskal, Phys. Rev. Letters 15 pp 240– (1965)
[21] Koosis, Acta Math. 116 pp 223– (1966)
[22] Lax, Comm. Pure Appl. Math. 28 pp 141– (1975)
[23] Lax, SIAM Revue (1976)
[24] Levitan, Amer. Math. Soc. 39 (1975)
[25] The inverse Sturm-Liouville problem, Mat. Tidsskr., B, 1949, pp. 25–30. · Zbl 0041.42310
[26] and , Hill’s Equation, Interscience-Wiley, New York, 1966. · Zbl 0158.09604
[27] McKean, Invenciones Mat. 30 pp 217– (1975)
[28] Finitely many mass points on the line under the influence of an exponential potential–an integrable system, Dynamical Systems Theory and Applications, ed. Springer-Verlag, New York, 1975, pp. 467–497. · Zbl 0323.70012
[29] Myrberg, Ann. Acad. Sci. Fennicae 14 pp 1– (1943)
[30] Myrberg, Acta Math. 76 pp 185– (1945)
[31] Novikov, Funkt. Anal. Pril. 8 pp 54– (1974)
[32] (Translation in Funct. Anal. pp 236– (1975)
[33] Topics in Complex Function Theory, Vol. II, Wiley-Interscience, New York, 1971.
[34] Sjöberg, J. Math. Anal. Appl. 29 pp 569– (1970)
[35] Weyl, Math. Ann. 77 pp 111– (1916)
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