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Saratov State Law Academy, Russia, 410056, Saratov, Volskaya st., 1, Oksana_Parlova@mail.ruA class of strongly irregular pencils of ordinary differential operators of second order with constant coefcients is considered. Theroots of the characteristic equation of the pencils from this class are supposed to lie on a straight line coming through the originand on the both side of the origin. Exact interval on which the system of eigenfunctions is 2-fold complete in the space of squaresummable functions is nded.Key words: quadratic pencil, second order pencil, pencil of ordinary differential operators, two-point boundary conditions,homogeneous differential expression with constant coefcients, completeness of the system of eigenfunctions, non-completenessof the system of eigenfunctions.

On 2-fold Completeness of the Eigenfunctions for the Strongly Irregular Quadratic Pencil of Differential Operators of Second Order