Solution of the inverse quasiperiodic problem for the Dirac system. (English. Russian original) Zbl 1235.34043

Nabiev, I. M.

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 \(p,q\in L_2(0,\pi)\).

Reviewer: Vjacheslav Yurko (Saratov)

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

Keywords:

Dirac operator; inverse spectral problem; quasiperiodic boundary conditions

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