Self‐Adjoint Differential‐Algebraic Operators With Boundary Terms

ABSTRACT In this paper, we introduce a class of self‐adjoint differential‐algebraic operators with boundary terms. The analytic structure of the resolvent of such an operator is investigated. Explicit representations of the eigenvectors of the initial operator are obtained; these eigenvectors form an orthogonal basis in the space . The system of eigenvectors is projected onto the subspace . It is shown that the projected system becomes a Riesz basis in only after removing a finite number of functions. A criterion is established that determines which functions should be removed from the projected system to ensure that the remaining functions form a basis.