Multiple non-completeness for the system of eigenfunctionsof a class of the pencils of ordinary differential operators

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 is supposed to lie on a straight line coming through the origin. The main condition is such that the generating functions for the system of eigen- and associated functions are linear combinations of exponential functions. The cases when the system of eigen- and associated functions is $n$-fold and $m$-fold ($3\le m\le n-1$) non-complete with infinity defect in the space of square summable functions on an arbitrary finite interval are described.