An explicit solution of the inverse periodic problem for Hill’s equation. (English) Zbl 0622.34021

Finkel, Allan; Isaacson, Eli; Trubowitz, Eugene

SIAM J. Math. Anal. 18, 46-53 (1987).

Let \(-d^ 2/dx^ 2+q(x)\) be the Hill’s operator with \(q\in L_{{\mathbb{R}}^ 2}(S^ 1)\). The authors give an explicit formula for the isospectral manifold of all potentials having the same spectrum as q.

Reviewer: H.Rüssmann

MSC:

34L99	Ordinary differential operators
34B30	Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34C25	Periodic solutions to ordinary differential equations

Keywords:

inverse problem; Hill’s operator; isospectral manifold; spectrum