On properties of the eigenfunctions of a quadratic pencil of the second order differential operators

The degenerated second order ordinary differential quadratic pencil with constant coefficients is considered. The case is studied, when the roots of characteristic equation lie on a straight line coming through the origin and on the both side of the origin. Properties of the system of its eigenfunctions in the spaces $L_2[0,\sigma]$, $\sigma>0$ is investigated. Criteria of one-fold completeness and minimality of this systemare proved and sufficient conditions of one-fold completeness and minimality are found.