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.

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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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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/

[1] Rykhlov V. S., “O kratnoi nepolnote sobstvennykh funktsii puchkov obyknovennykh diferentsialnykh operatorov”, Matematika. Mekhanika. Sb. nauch.tr., 3, Izd-vo Sarat. un-ta, Saratov, 2001, 114–117

[2] Rykhlov V. S., “O kratnoi nepolnote sobstvennykh funktsii puchkov differentsialnykh operatorov, korni kharakteristicheskogo uravneniya kotorykh lezhat na odnom luche”, Dokl. RAEN, 2004, no. 4, 72–79

[3] Golub A. V., Kutepov V. A., Rykhlov V. S., Kratnaya nepolnota sobstvennykh funktsii puchkov differentsialnykh operatorov, korni kharakteristicheskogo uravneniya kotorykh lezhat na odnom luche, Dep. v VINITI 05.08.04. No 1353-V2004, Saratov, 2004, 24 pp.

[4] Rykhlov V. S., Shigaeva O. V., “Ob $n$-kratnoi nepolnote sistemy sobstvennykh funktsii odnogo klassa puchkov differentsialnykh operatorov”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tez. dokl. 14-i Sarat. zimn. shkoly, Izd-vo Sarat. un-ta, Saratov, 2008, 162

[5] Rykhlov V. S., Shigaeva O. V., “Teorema o kratnoi nepolnote kombinatsii eksponent s pokazatelyami, lezhaschimi na odnoi pryamoi, i ee primenenie k puchkam differentsialnykh operatorov”, Matematika. Mekhanika: Sb. nauch. tr., 10, Izd-vo Sarat. un-ta, Saratov, 2008, 69–72

[6] Rykhlov V. S., “O polnote sobstvennykh funktsii odnogo klassa differentsialnykh operatorov s postoyannymi koeffitsientami”, Izv. vuzov. Matematika, 2009, no. 6, 42–53 | MR | Zbl