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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 $$ -y''+q(x)y=\lambda y,\quad 0<x<1, $$ $$ y(0)\cos\alpha=y'(0)\sin\alpha,\quad y'(1)=f(\lambda)y(1). $$ Here, $q\in AC[0,1]$, $\alpha\in[0,\pi)$, $f(\lambda)=h(\lambda)/g(\lambda)$, 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.

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