Plaksina, O. A. Inverse problems of the spectral analysis for Sturm-Liouville operators with nonseparated boundary conditions. (Russian) Zbl 0631.34028 Mat. Sb., N. Ser. 131(173), No. 1(9), 3-26 (1986). 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 Cited in 3 ReviewsCited in 10 Documents MSC: 34L99 Ordinary differential operators Keywords:inverse problems; spectral analysis; Sturm-Liouville operators PDFBibTeX XMLCite \textit{O. A. Plaksina}, Mat. Sb., Nov. Ser. 131(173), No. 1(9), 3--26 (1986; Zbl 0631.34028) Full Text: EuDML