On a nonlocal perturbation of a periodic eigenvalue problem

Abstract

It is well known that the system of eigenfunctions of a formally self-adjoint differential operator with arbitrary self-adjoint boundary conditions providing a point spectrum is an orthonormal basis in the space L2. The problem as to whether the basis property is preserved under a weak, in a sense, perturbation of the original self-adjoint operator with discrete spectrum was considered in numerous papers (e.g., see [1, 2]). For a nonself-adjoint operator whose system of root functions is a Riesz basis in L2, a similar problem was investigated in [3]. In the present paper, on the interval [0, 1], we consider the problem