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On a Hill's equation with double eigenvalues


Author: Harry Hochstadt
Journal: Proc. Amer. Math. Soc. 65 (1977), 373-374
MSC: Primary 34B30
DOI: https://doi.org/10.1090/S0002-9939-1977-0445059-8
MathSciNet review: 0445059
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Abstract: Let $ \Delta (\lambda )$ be the discriminant of a Hill's equation with a $ \pi $-periodic potential $ q(x)$. It is shown that if $ 2 + \Delta (\lambda )$ has only double zeros then $ q(x)$ is necessarily $ \pi /2$-periodic.

References [Enhancements On Off] (What's this?)

  • [1] G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math. 78 (1946), 1-96. MR 0015185 (7:382d)
  • [2] H. Hochstadt, On the determination of a Hill's equation from its spectrum, Arch. Rational Mech. Anal. 19 (1965), 353-362. MR 0181792 (31:6019)
  • [3] -, On the theory of Hill's matrices and related inverse spectral problems, Linear Algebra and Appl. 11 (1975), 41-52. MR 0422921 (54:10906)

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DOI: https://doi.org/10.1090/S0002-9939-1977-0445059-8
Article copyright: © Copyright 1977 American Mathematical Society

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