Geodesic
On multiple completeness of the root functions of ordinary differential polynomial pencil with constant coefficients
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 63 (2017) no. 2, pp. 340-361

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In the space of square integrable functions on a finite segment we consider a class of polynomial pencils of $n$th-order ordinary differential operators with constant coefficients and two-point boundary-value conditions (at the edges of the segment). We suppose that roots of the characteristic equation of pencils of this class are simple and nonzero. We establish sufficient conditions for $m$-multiple completeness ($1\le m\le n$) of the system of root functions of pencils from this class in the space of square integrable functions on this segment. 
@article{CMFD_2017_63_2_a6,
     author = {V. S. Rykhlov},
     title = {On multiple completeness of the root functions of ordinary differential polynomial pencil with constant coefficients},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {340--361},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a6/}
}
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V. S. Rykhlov. On multiple completeness of the root functions of ordinary differential polynomial pencil with constant coefficients. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 63 (2017) no. 2, pp. 340-361. http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a6/