On multiple completeness of the root functions of the pencils of differential operators with constant coefficients

A class of the pencils of ordinary differential operators of $n$-th order with constant coefficients is considered. The roots of the characteristic equation of the pencils from this class are supposed to lie on a straight line containing the origin, provided that one of the roots lies on one part from the origin, the rest lie on another part. The cases when the system of root functions is $m$-fold $(3\leq m\leq n-1)$ complete in the space of square summable functions on main interval are described.