Article
Ufa Mathematical Journal
Volume 3, Number 3, pp. 78-89
On approximation properties of the root functions generated with the correctly solvable boundary value problems for the high order ordinary differential equations
Kanguzhin B.E., Nurakhmetov D.B., Tokmagambetov N.E.
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In this work the properties of systems of root functions generated correctly solvable boundary value problems for higher order ordinary differential equations are studied. The biorthogonal systems of functions corresponding to the system of root functions are constructed. The found systems of root functions are minimal systems. And completeness in $ L_ {2} (0,1)$ of the systems of root functions is proved. The algorithm for the inverse problem is given by reconstruction of the boundary functions. And also some identities found for the eigenvalues of the considered operator.