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Malamud","submitted_at":"2018-07-14T07:19:41Z","abstract_excerpt":"The paper is concerned with completeness property of rank one perturbations of unperturbed operators generated by special boundary value problems (BVP) for the following $2 \\times 2$ system \\begin{equation}\n  L y = -i B^{-1} y' + Q(x) y = \\lambda y , \\quad\n  B = \\begin{pmatrix} b_1 & 0 \\\\ 0 & b_2 \\end{pmatrix}, \\quad\n  y = \\begin{pmatrix} y_1 \\\\ y_2 \\end{pmatrix}, \\end{equation}\n  on a finite interval assuming that a potential matrix $Q$ is summable, and $b_1 b_2^{-1} \\notin \\mathbb{R}$ (essentially non-Dirac type case). 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