Abstract.

In this paper, we consider some properties of the systems of root functions generated by the first order differential operator. We obtain explicit form of the biorthogonal systems for the systems of root functions generated by the first order differential operator. We investigate the approximation properties of the systems of root functions of the first order differential operator. We obtain a suficient condition for the completeness of the systems of root functions of the first order differential operator in terms of the boundary functions.

Keywords:

resolvent of the operator, well-posed boundary value problems, completeness of the systems of root functions.