ON BASIS PROPERTY OF SYSTEMS ROOT VECTORS OF A LOADED MULTIPLE DIFFERENTIATION OPERATOR

Аннотация

In the case of non-self-adjoint ordinary differential operators, the basis property of systems of
eigenfunctions and associated functions (E&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&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.
In Sadybekov M.A., Imanbaev N.S., we studied another version of the non-self-adjoint perturbation of the selfadjoint 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.
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&AF)
systems of a loaded multiple differentiation operator is studied.