On a Hill’s equation with double eigenvalues

Hochstadt, Harry

doi:10.1090/S0002-9939-1977-0445059-8

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 . It is shown that if $2 + \Delta (\lambda )$ has only double zeros then is necessarily $\pi /2$ -periodic.

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[2] Harry Hochstadt, On the determination of a Hill’s equation from its spectrum, Arch. Rational Mech. Anal. 19 (1965), 353–362. MR 0181792, https://doi.org/10.1007/BF00253484
[3] Harry Hochstadt, On the theory of Hill’s matrices and related inverse spectral problems, Linear Algebra and Appl. 11 (1975), 41–52. MR 0422921

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