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Equivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. (English) Zbl 1046.34021

Inverse spectral problems are considered for the boundary value problem

-y '' +q(x)y=λy,0<x<1,
y(0)cosα=y ' (0)sinα,y ' (1)=f(λ)y(1)·

Here, qAC[0,1], α[0,π), f(λ)=h(λ)/g(λ), where g and h are polynomials with real coefficients and no common zeros. Uniqueness theorems are proved for two inverse problems of recovering the potential q and the coefficients of the boundary conditions from the Weyl function and from two spectra.

34A55Inverse problems of ODE
34B24Sturm-Liouville theory
34B07Linear boundary value problems with nonlinear dependence