On a Hill’s equation with double eigenvalues
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- by Harry Hochstadt
- Proc. Amer. Math. Soc. 65 (1977), 373-374
- DOI: https://doi.org/10.1090/S0002-9939-1977-0445059-8
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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
- Göran Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Math. 78 (1946), 1–96 (German). MR 15185, DOI 10.1007/BF02421600
- Harry Hochstadt, On the determination of a Hill’s equation from its spectrum, Arch. Rational Mech. Anal. 19 (1965), 353–362. MR 181792, DOI 10.1007/BF00253484
- Harry Hochstadt, On the theory of Hill’s matrices and related inverse spectral problems, Linear Algebra Appl. 11 (1975), 41–52. MR 422921, DOI 10.1016/0024-3795(75)90116-0
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- 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