Geodesic
On multiple completeness of the root functions for a~class of the pencils of differential operators
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 2, pp. 24-34

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A polinomial pencil of ordinary differential operators of $n$-th order generated by a homogeneous differential expression with constant coefficients and by two-point boundary conditions of a special structure with $l$ conditions in zero only ($1\le l\le n-1$) is considered in the space $L_2[0,1]$. The case is studied, when the roots of the characteristic equation lie on a ray coming fromthe origin. A sufficient condition of $m$-fold completeness of the system of root functions for $m\le n-l$ in the space $L_2[0,1]$ is found. An accuracy of obtained result is shown. 
@article{ISU_2010_10_2_a3,
     author = {V. S. Rykhlov},
     title = {On multiple completeness of the root functions for a~class of the pencils of differential operators},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {24--34},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2010_10_2_a3/}
}
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V. S. Rykhlov. On multiple completeness of the root functions for a~class of the pencils of differential operators. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 2, pp. 24-34. http://geodesic.mathdoc.fr/item/ISU_2010_10_2_a3/