Geodesic
On properties of the eigenfunctions of a quadratic pencil of the second order differential operators
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 1, pp. 31-44 
V. S. Rykhlov. On properties of the eigenfunctions of a quadratic pencil of the second order differential operators. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 1, pp. 31-44. http://geodesic.mathdoc.fr/item/ISU_2009_9_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The degenerated second order ordinary differential quadratic pencil with constant coefficients is considered. The case is studied, when the roots of characteristic equation lie on a straight line coming through the origin and on the both side of the origin. Properties of the system of its eigenfunctions in the spaces $L_2[0,\sigma]$, $\sigma>0$ is investigated. Criteria of one-fold completeness and minimality of this systemare proved and sufficient conditions of one-fold completeness and minimality are found.

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