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Solution of the inverse quasiperiodic problem for the Dirac system. (English. Russian original) Zbl 1235.34043
Math. Notes 89, No. 6, 845-852 (2011); translation from Mat. Zametki 89, No. 6, 885-893 (2011).
The characterization of the spectrum is given for the boundary value problem \[ By'(x)+\Omega(x)y(x)=\lambda y(x),\; 0<x<\pi,\; y(\pi)=e^{it}Y(0), \] \[ y=\left[ \begin{matrix} y_1 \\ y_2 \end{matrix}\right],\quad B= \left[ \begin{matrix} 0 & 1 \\ -1 & 0 \end{matrix}\right],\quad \Omega(x)= \left[ \begin{matrix} p(x) & q(x) \\ q(x) & -p(x) \end{matrix}\right], \] where \(p(x), q(x), t\) are real, and \(p,q\in L_2(0,\pi)\).

MSC:
34A55 Inverse problems involving ordinary differential equations
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
34L05 General spectral theory of ordinary differential operators
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