Geodesic
On a problem that does not have basis property of root vectors, associated with a perturbed regular operator of multiple differentiation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 568-573

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A spectral problem for a multiple differentiation operator with integral perturbation of boundary value conditions which are regular but not strongly regular is considered in the paper. The feature of the problem is the absence of the basis property of the system of root vectors. A characteristic determinant of the spectral problem is constructed. It is shown that absence of the basis property of the system of root functions of the problem is unstable with respect to the integral perturbation of the boundary value condition.
Keywords: multiple differentiation operator, integral perturbation of boundary value conditions, basis property, root vectors, system of eigenfunctions and associated functions, eigenvalue, characteristic determinant. 
@article{JSFU_2020_13_5_a4,
     author = {Nurlan S. Imanbaev},
     title = {On a problem that does not have basis property of root vectors, associated with a perturbed regular operator of multiple differentiation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {568--573},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a4/}
}
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Nurlan S. Imanbaev. On a problem that does not have basis property of root vectors, associated with a perturbed regular operator of multiple differentiation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 568-573. http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a4/