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Inverse problems of the spectral analysis for Sturm-Liouville operators with nonseparated boundary conditions. (Russian) Zbl 0631.34028

The author considers inverse problems of the spectral analysis for Sturm- Liouville operators of type \(-d^ 2/dx^ 2+q(x),\) \(x\in [0,\pi]\), with nonseparated boundary conditions of the form: \[ y(0)+\omega y(\pi)=0,\quad {\bar \omega}y'(0)+\alpha y(\pi)+y'(\pi)=0, \]
\[ \beta y(0)+y'(0)+\omega y(\pi)=0,\quad -{\bar \omega}y(0)+\gamma y(\pi)+y'(\pi)=0. \] where \(\alpha\), \(\beta\), \(\gamma\) are real numbers and \(\omega\neq 0\) is an arbitrary complex number. For both sets of boundary conditions necessary and sufficient conditions for the existence of a unique differential operator, which satisfies the described conditions, are given.
Reviewer: D.Herceg

MSC:

34L99 Ordinary differential operators
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