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Sturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter. II. (English) Zbl 1019.34028
Summary: Necessary and sufficient conditions are given for two sequences $\lambda _n$ and $\rho _n$ to be the eigenvalues and norming constants of the Sturm-Liouville boundary value problem $-y''+qy={\lambda}y$, $y(0)\cos{\alpha}=y'(0)\sin{\alpha}$ and $y'(1)=f({\lambda})y(1)$, where $f$ is a rational function of Herglotz-Nevanlinna type. It is also proved that $q$,$\alpha$ and $f$ are uniquely determined by the sequences ${\lambda}_n$ and ${\rho}_n$. For part I see the review above.

34B24Sturm-Liouville theory
34L05General spectral theory for OD operators
Full Text: DOI
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