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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.

MSC:

34B24 Sturm-Liouville theory
34L05 General spectral theory of ordinary differential operators
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