@article{Imanbaev_2020, title={ON BASIS PROPERTY OF SYSTEMS ROOT VECTORS OF A LOADED MULTIPLE DIFFERENTIATION OPERATOR}, url={https://journals.nauka-nanrk.kz/physics-mathematics/article/view/389}, abstractNote={<p>In the case of non-self-adjoint ordinary differential operators, the basis property of systems of eigenfunctions and associated functions (E&amp;AF), in addition to the boundary value conditions, can be affected by values of coefficients of the differential operator. Moreover, it is known that the basic properties of E&amp;AF can be changed at a small change of values of the coefficients. This fact was first noted in V.A. Il’in. Ideas of V.A. Il’in for the case of non-self-adjoint perturbations of the self-adjoint periodic problem were developed in A.S. Makin where operator was changed due to perturbation of one of the boundary value conditions.<br>In Sadybekov M.A., Imanbaev N.S., we studied another version of the non-self-adjoint perturbation of the self-adjoint periodic problem. In contrast to A.S. Makin, in Sadybekov M.A. and Imanbaev N.S. perturbation occurs due to the change in the equation, which belongs to the class of so-called loaded differential equations, where the basic properties of root functions are investigated.<br>In this paper we consider perturbations of a second order differential equation of the spectral problem with a loaded term, containing a value of the unknown function at the point zero, with regular, but not strongly regular boundary value conditions. Question about basis property of eigenfunctions and associated functions (E&amp;AF) systems of a loaded multiple differentiation operator is studied.</p>}, number={1}, journal={Известия НАН РК. Серия физико-математическая}, author={Imanbaev, N.S.}, year={2020}, month={фев.}, pages={32–37} }