On Multiple Completeness of the Root Functions of a Certain Class of Pencils of Differential Operators with Constant Coefficients

We consider the class of pencils of ordinary differential operators of $n$-th order with constant coefficients. It is assumed that the roots of the characteristic equation of pencils from this class are simple, non-zero and lie on the same straight line passing through the origin. Sufficient conditions for $n$-fold completeness of the system of root functions of the pencils from this class in the space of summable with square functions on the main segment are formulated.