Geodesic
Multiple non-completeness for the system of eigenfunctionsof a class of the pencils of ordinary differential operators
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 50-59 
O. V. Shigaeva. Multiple non-completeness for the system of eigenfunctionsof a class of the pencils of ordinary differential operators. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 50-59. http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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