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 × 2 system 1991 Mathematics Subject Classification. Primary 47E05; Secondary 34L10, 47B15. Key words and phrases. Systems of ordinary differential equations, normal operator, completeness of root vectors, resolvent operator, rank one perturbation, Riesz basis property.

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