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

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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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     author = {V. S. Rykhlov},
     title = {On properties of the eigenfunctions of a~quadratic pencil of the second order differential operators},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_1_a4/}
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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/