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An inverse problem for a Hill’s equation. (English) Zbl 0333.34017

Summary: A Hill’s equation defined on a semi-infinite interval will in general have a mixed spectrum. The continuous spectrum will in general consist of an infinite number of disjoint finite intervals. Between these intervals, point eigenvalues can exist. It is shown that under suitable hypotheses on the spectrum a full knowledge of the spectrum leads to a unique determination of the potential function in the Hill’s equation.

MSC:

34L05 General spectral theory of ordinary differential operators
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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