On multiple completeness of the root functions for a class of the pencils of differential operators

A polinomial pencil of ordinary differential operators of $n$-th order generated by a homogeneous differential expression with constant coefficients and by two-point boundary conditions of a special structure with $l$ conditions in zero only ($1\le l\le n-1$) is considered in the space $L_2[0,1]$. The case is studied, when the roots of the characteristic equation lie on a ray coming fromthe origin. A sufficient condition of $m$-fold completeness of the system of root functions for $m\le n-l$ in the space $L_2[0,1]$ is found. An accuracy of obtained result is shown.