Direct Problem of Scattering Theory for a DiracSystem of Differential Equations on the Half-Linein the Case of Finite Density

In this paper, we study the direct scattering problem on the half-line for the Dirac system of differential equations in the case of finite density with the boundary condition $$y_{1}(0)=y_{2}(0) $$ . The spectrum is studied, the resolvent is constructed, and the spectral expansion in the eigenfunctions of the Dirac operator is obtained.

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